I can hide inside the image of a barrel, right?

I'm sure this has come up before: I can cast Minor Illusion to create the illusion of a large barrel or box or whatever, and then hide inside the image (I'm a gnome, so shorter than 5').

Enemies would specifically need to take the study action to determine the barrel isn't real, at which point I'd be visible to them. But until then, and for the next minute, I could be firing my crossbow (no verbal component to give away my position, though I suppose the twang of my crossbow might be audible). 

Similarly I could hide our bard or an NPC, right?

Yes, that should work, and it's a common use of Minor Illusion. 

However, depending on what sort of enemies you're fighting, it may not be reasonable to assume that they won't figure out roughly where you are after your first attack.

Quote from MongooseGef >>

I'm sure this has come up before: I can cast Minor Illusion to create the illusion of a large barrel or box or whatever, and then hide inside the image (I'm a gnome, so shorter than 5').

Enemies would specifically need to take the study action to determine the barrel isn't real, at which point I'd be visible to them. But until then, and for the next minute, I could be firing my crossbow (no verbal component to give away my position, though I suppose the twang of my crossbow might be audible). 

Similarly I could hide our bard or an NPC, right?

 Probably any short creature could hide. Your DM might make you roll a stealth check to stay hidden (especially after firing the crossbow), but it could work, especially for an ambush of some sort.

Yeah, an ambush is what I'm expecting this tactic to be used for primarily. Anything to give me an extra round or two where I can attack but the enemy can't!

You can hide, but there's some ambiguity as to what you can do without revealing the illusion. The way I see it, shooting through the illusion counts as physical interaction. If someone sees a bolt fly through the object, they will know it's an illusion.

Quote from MongooseGef >>

Yeah, an ambush is what I'm expecting this tactic to be used for primarily. Anything to give me an extra round or two where I can attack but the enemy can't!

 If you attack through it, they will know it is an illusion. I've used minor illusion to hide my gnome druid at low levels but the monsters we have fought the last few levels (we are 10 now) are way to smart to fall for the trick.  maybe if you're in a room full of barrels (mimics used that trick in a different campaign)...even then maybe not.

Quote from Foodgeek >>

Quote from MongooseGef >>

Yeah, an ambush is what I'm expecting this tactic to be used for primarily. Anything to give me an extra round or two where I can attack but the enemy can't!

 If you attack through it, they will know it is an illusion. I've used minor illusion to hide my gnome druid at low levels but the monsters we have fought the last few levels (we are 10 now) are way to smart to fall for the trick.  maybe if you're in a room full of barrels (mimics used that trick in a different campaign)...even then maybe not.

Quote from Frachese >>

You can hide, but there's some ambiguity as to what you can do without revealing the illusion. The way I see it, shooting through the illusion counts as physical interaction. If someone sees a bolt fly through the object, they will know it's an illusion.

I disagree with this. The enemy has to physically interact with the illusion to automatically disbelieve it.  That is, they have to literally walk up and poke it (or poke it with something they're physically touching) to know that it actually went through the object without resistance, not just close to it.  (If they're throwing something at the illusion to see if it passes through, that should be a study action).  Letting everyone who thinks they see something pass through an illusion automatically disbelieve it makes illusion magic far too weak. 

(I will agree the rules passages to this effect are readable both ways, but it makes far more sense for the 'accidental' discovery that something is an illusion to be a bit more involved than just seeing something far from you - whereas if your hand passes through it, you know it's not real.  That's what physical interaction should look like.  If it would just make them think 'huh, that was weird', that's grounds for investigation, not automatic disbelief.  And i think this is the better reading too, because belief or disbelief in the illusion is decided individually for each creature, so the physical interaction should be individual for each creature).

So seeing a crossbow bolt come from vaguely the direction of a barrel 60' away might not even be suspicious.  Maybe someone is behind the barrel and popped up to fire over it.  It might give him reason to suspect its an illusion, especially the second time it happens, when he's paying more attention to the barrel because he suspects someone is behind it, and doesn't see anyone pop up. (and that would allow him to take the study action - i wouldn't even let him make a study action unless something gave him a reason to be suspicious).

That said, you can't be hidden and firing your crossbow, because making an attack roll ends Hidden.  The enemy knows approximately where you are - enough to make an attack against you.  That doesn't mean he can see you.  (A minor illusion which completely blocks your body should count as being heavily obscured).  You are still unseen, and should get advantage on attack rolls, even though you're not hidden.

If you pop up/around and shoot, you won't be unseen, but you should prevent the enemy from even taking the study action, because they'll have no reason to suspect it's an illusion.

But really, talk to your DM on how they think illusions work.