Bonus actions,  do you add the modifier you would normally get from dex and proficiency. My dm has never let me add the modifier to bonus attacks but dnd beyond allows there Furry of blows yo add the modifier and I'm wonder why and how. I dont see any rule that allows the person to use the modifier without two weapon fighting

Monk is kind of unique to this but I have read a few times (and we play by the rule) that the BA unarmed strike is a full out unarmed strike with all bonuses applied.  It's part of being a Monk, getting that perk, although it DOES depend on you making an Attack with either a Monk weapon OR an unarmed attack.  If you use an item or cast a spell (multi classing or feats and such) as your action, you do not get to make the unarmed strike as BA.

FoB is a Ki powered feature, thus is a special attack with rules of it's own, so 2 weapon fighting and so forth have no impact.  

On a side note, my Monk has a pair of boots that I can activate to ZOOM into a foe, dealing impact damage.  I roll an Athletics check to take 1/4 of that damage, and take 1/2 the dealt damage on a fail.  Our DM has ruled that if I use the boots as an action, I can do 1 unarmed strike as BA, but not FoB because I did not use a Monk weapon or unarmed to attack.  (could argue I used an actual Monk to do the attacks, but......)

When you make an attack, you get to add the modifier. That's the normal rule.

TWF explains that if you use it, you don't get to add the modifier to the bonus action attack - that's an exception to the normal rule.

Martial Arts doesn't have the exception that TWF does, and neither does Flurry of Blows, so the normal rule applies and you get to add the modifier to these bonus action attacks.

TL;DR - Add your modifier to the damage for unarmed strikes if you are a monk.

It's explained in the Martial Arts section of the monk class features. The important part reads;

"When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action."

This is different from two weapon fighting, as that reads;

"When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.''

Because you are gaining the ability to make the unarmed strike through your monk feature and not two weapon fighting you do not have to abide by the restriction of not adding your ability modifier.

Scenario: You take the Attack action and attack with a quarterstaff, then wish to follow it up with an unarmed strike as a bonus action. Two weapon fighting CANNOT even be applied here as the quarterstaff doesns't have the light property, so the rule of not adding your modifier to the unarmed strike cannot even be argued for as you are not engaging that rule. Even if you take the attack action and attack with a weapon that has the light property, such as a dagger or shortsword, you have to make the unarmed strike as a bonus action through the use of the monk feature and not two weapon fighting as your unarmed strikes do not have the light property.

Quote from GreyJedi70 >>

Bonus actions,  do you add the modifier you would normally get from dex and proficiency. My dm has never let me add the modifier to bonus attacks but dnd beyond allows there Furry of blows yo add the modifier and I'm wonder why and how. I dont see any rule that allows the person to use the modifier without two weapon fighting

You apply the modifier to weapon attacks unless an effect specifies otherwise. The normal rule for two weapons specifies that you don't apply the ability score to damage, but effects such as monk martial arts, bonus action attacks from crossbow expert, great weapon mastery, polearm mastery, and the like, do not have any such restrictions, and thus you add your ability score.

You are not making an off hand attack as a bonus action.
TWF differentiates between a weapon you have in one hand that you use as part of the attack action and another weapon you have in the other hand that you can use as a bonus action. 

Monk’s martial arts makes no differentiation. All unarmed strikes and monk weapon attacks apply the modifier. Unless it says otherwise, which it doesn’t.