Judd, I am not sure what the bubbles are. It sounds like solvent pop. If you have a magnifying glass to see real close look to see if they look like a volcano with a little ridge around the hole. Also more should be on the top surfaces. This would be solvent pop or air intrapment, though solvent pop would be much more likely. The top of the paint seals off while solvent is trapped in the lower coats. When the solvent breaks through it leaves that little ring.
If there is less of them and they do not have that little ring but simply look like a hole. And are a little larger like 1/16" or so and usually in patterns and not all over it would likely be fish eye.
If it is either one needs to be sanded down quite a bit. If it is solvent pop, they can sometimes be sanded out and buffed. If it is fish eye it is damaged down deep into the paint and needs to be just about all sanded off and repainted.
I don't think peeling is going to be a problem. The only way that would be an issue is if they guy cuts and buffs the solvent pop out and thins the paint too much leaving it with little UV protection.
I would say, you need to get some sort of guarantee that you paint will be as good as it would be if this had not happened.
