I play as a druid and just realized that I can move Flaming Sphere as a bonus action. My idea is to transform into either a giant constrictor snake or giant octopus, grapple an enemy from one side, and then ram the enemy with the flaming sphere from the other side while holding them in place. While they remain grappled, they would take damage from me, damage from the sphere during my bonus action, and then additional damage from the sphere when they end their turn in its area of effect.

Thinking in terms of squares this should work, since the creature would occupy the five feet between myself and the sphere. Logically though, if I'm constricting a creature part of my body would be occupying the enemy's space, so I would theoretically also take fire damage at the end of my turn.

So in short my question is, when I grapple a creature as a beast do I share its space?

RAW I think you would be fine. But as you said, logically part of your body is in their space. I would probably let you do it once without damage based on rule of cool, but you would take damage as well in subsequent fights.

Well, it does say "any creature" in regards to damage, so if you are a snake or octopus when doing as you propose, you would be damaged too.

However, grappling as a human(oid) doesnt necessarily mean you have to have your limbs surrounding your opponent, so if you grapple as a humanoid or similar (such as a bear, ape, etc) you could hold the enemy in place while staying outside the range of the sphere.

You do not occupy the same space as the creature you are grappling. You would not take damage from the Sphere as long as it was on the opposite side of the Target. So it would work like  X    Y    Z

X = Sphere

Y = Target

Z = You

Yes, in terms of general play, but if you use a creature that must wrap part of itself around the target to grapple, it could be reasonably argued that grappling in such a way makes you vulnerable to area effects that affect the target, thus you would want to use a form that is not required to wrap itself.

I read quite a few articles to make sure I didn't have my info wrong. Also, I've played as a druid many times and know flaming sphere well. And I have a few concerns.

Wild Shape: "Starting at 2nd level, you can use your action to magically assume the shape of a beast that you have seen before. You can use this feature twice. You regain expended uses when you finish a short or Long Rest."

Flaming Sphere: "...As a Bonus Action, you can move the Sphere up to 30 feet..." Casting time: 1 action

Actions in Combat: "When you take your action on your turn, you can take one of the actions presented here, an action you gained from your class or a special feature, or an action that you improvise:.....Each spell has a casting time, which specifies whether the caster must use an action, a reaction, minutes, or even hours to cast the spell. Casting a spell is, therefore, not necessarily an action. Most spells do have a casting time of 1 action, so a spellcaster often uses his or her action in combat to cast such a spell."

Going off of all this material,  I do not think this attack is possible. Even if you are in Circle of the Moon, letting wild shape be your bonus action, and thus having the spell be your action, you cannot then take a second action to wield the sphere. Therefore you would have to take a second turn in order to wield the sphere and depending on how many people are initiative order, your spell may end before you have a chance to. Even if you do, people would clearly be able to tell that you're going to attempt to wield the sphere later on once the spell is cast. 

I apologize for derailing your idea, and I don't mean to sound condescending, I just don't want you getting in trouble with your DM. 

@daisyanam um, one issue, turns are parallel, not sequence, so the person using Wildshape and Flaming Sphere would still have 4-5 turns to wield the sphere.

I was going to suggest looking at other forms to see if there is anything with Fire resistance or immunity, but the only options with resistance have less than half the hit points of your options, making it a bit redundant.

Immunity has nothing until Fire Elemental at level 10.

It's worth asking your DM on their interpretation as it's really the only one that matters as to how they'll treat the grapple.

Have you considered Sentinel instead of grappling? If they attempt to move, you get to make an opportunity attack to drop their speed to 0. They also can't use Disengage.

Why would the turns be parallel? At least in every campaign I've been in we've just done initiative order

@daisynam I need to clarify, everyone takes their turns in sequence following the initiative order, but the characters are acting parallel, so every turn taken during the first round occurs within 6 seconds of the encounter starting, so if you have 10 creatures in the encounter, it is not 1 minute for each time they all act, it is only 6 seconds.

I say this only because you stated that if the control of the sphere had to happen on the second turn, the player may not be able to due to time, which is not standard play, and in fact drastically affects game balance.

I was going off of the basis that each turn is 6 seconds. What I'm saying is if she were to take one 6 second turn and cast flaming sphere and turn into an animal, she'd have to wait until her next 6 second turn to do something with the sphere. She can eventually do something with the sphere she'd just have to wait until her next 6 second turn, she can't turn into an animal, cast flaming sphere, pick up a person, and hurl the sphere at them. That's best case scenario with circle of the moon still 2 actions and 2 bonus actions

You are correct that each turn is 6 seconds, and the player would have to wait till turn 2 before gaining control of the sphere. The reason I commented about time and turns, is that your statement:

Therefore you would have to take a second turn in order to wield the sphere and depending on how many people are initiative order, your spell may end before you have a chance to.

Would seem to indicate that you count 10 creature turns per minute, when the proper way is 10 rounds of turns per minute. To put it another way, a person that casts a spell with duration 1-minute has 10 of their own turns to utilize the spell, not 10 turns divided among all creatures within that encounter.

You don't have that accurate.  A ROUND is 6 seconds.  Each persons turn takes place "at the same time", theoretically speaking.  As Journer said, you seem to think having 10 creatures in combat would make a Round last a full minute, and thus cause any spells that last a minute dispell before your next turn.  This is not the case.  A spell with a duration of 1 minute lasts 10 rounds of combat, no matter how many creatures there are in the initiative order.  If you're playing as though turns are sequential, you are seriously limiting all spellcasters.

RAW, what Kyrei is wanting to do would work perfectly well, and is a great idea for druids.  If the DM wants to say that you're in the creatures space that's up to them, particularly if you're playing in the theater of the mind, but on a grid you would still be 2 squares (10 feet) away from the flaming sphere while grappling a creature the sphere is on the opposite side of, and thus you wouldn't take any damage and could, for up to 9 rounds after the initial cast, cause them to take damage from it.  You don't even need to ram it into them as a bonus action, they're standing next to it so they're going to take damage anyway at the end of their turn.  But as Kyrei says, ramming it into them will cause even more damage.
This is a very effective tactic.

I'd say you could fudge this idea by specifying how you're grappling the opponent. When a humanoid grapples it's assumed that they're just holding onto the enemy somehow with one hand, preventing the opponent from moving and allowing the player to still attack with their free hand.  So if you assume that your constrictor snake is completely wrapped around the opponent, yeah it makes sense to take a little damage from the sphere. But if you think of it more as using the end of your tail to hold onto their legs, then you could logistically say that you're holding the enemy still while still keeping enough of your body out of the range of the sphere to avoid damage.

Did a little more looking, and while you could not be a Giant Constrictor Snake (it is CR 2, and Wild Shape only allows up to CR 1), you could indeed be the Giant Octopus, and do as you propose, and here is how I would word it:

After using Wild Shape less than 1 hour prior to the use of Flaming Sphere: get within 15 feet of target, then say "I attack the (insert target here) with my tentacles, using the suckers to grapple them and keep them just within range of the Flaming Sphere"

Then go ahead and hold them there for the duration, or until they succeed on a DC 16 Athletics or Acrobatics check, or till they die.

Sounds like this will be up to my DM.

But if you think of it more as using the end of your tail to hold onto their legs, then you could logistically say that you're holding the enemy still while still keeping enough of your body out of the range of the sphere to avoid damage.

This is a good idea, I'll bring it up this way. It doesn't make sense to use the standard 3x3 block to represent the giant snake, but that's what we've done in the past. No reason we'd change it now. I think I can make a reasonable case.

As an aside, I'm aware it will take two rounds to do damage; I usually cast a concentration spell and then transform as my bonus action before attacking in round 2. With conjure animals, faerie fire, barkskin, etc I don't do damage on my first turn but its worth it over time.

Edit: I just saw Journer's post. I'm Circle of the Moon, which gives you access to higher CR beasts. I agree though that the octopus would be easier to visualize, and it also has a 15 ft reach to grab, so its body would be well out of range.

There's nothing about the Grappled that requires any part of your body be wrapped around the target's. You can grapple someone by simply grabbing hold of their clothing or armor which restricts their movement. Holding someone's back against the flame doesn't necessarily mean your hand is in the flame as well.