Trying to figure out why I seem to get bubbles in the paint on my models

You might want to give Aaron Skinner's How To:  a look it may help clear some of the confusion. 

http://www.finescale.com/en/Videos/How%20To/2012/05/Basic%20Airbrushing%20Techniques.aspx

Good Luck and keep those questions coming in.

The biggest advice to folks new to airbrushing is... practice, practice, practice!  I recommend folks practice for at least a half hour- an hour would be better- on scrap before trying on a good model.  This should allow you to find optimum thinning ratios, which materials require prime and which don't, best pressures, best distances (airbrush nozzle from surface being painted), and best movement speed.

While you can inquire about things like thinning ratios, pressures, etc., it depends a lot on your own motions, stroke speeds and such, so recommended thinning, pressures, distances, are just general starting points that have to be refined for each person and type of equipment. Airbrushing is an art, not a mechanical skill that has fixed, simple rules.

Also, consider an airbrush a kind of brush that applies brushmarkless finish, not a kind of spray gun that speeds up painting.  Use low pressures, low flow rates, and go slowly. Never attempt to rush airbrushing, and use multiple coats of most finishes.

With the paint lifting, I have to wonder if you omitted the very important step of washing the plastic a) before assembly and b) quickly before painting?  Personally, I wash everything on the sprues in soapy water, wash them clean, and spray them down with ISO alcohol, allowing it all to dry a day before I start on anything.  Second, after I'm finished with assembly and prior to paint, I give it all another light spray of ISO alcohol just to clean any finger oils left by handling.  Then I shoot my primer, then I paint.

As mentioned above, a moisture trap is important, and check and drain it often.  Thinning ratio is important, as is using a suitable thinner for the paints.  (you've not really mentioned what type of paint you've used, though...)

Hope that helps.

paint pulling away from the edges could also mean you are spraying too thin a mixture and trying to put too thick a coat on. especially if its gloss paint. as reaper said a primer coat will help too, if you are missing it out.

First not to knock you or anything......but wood is different than plastic. Its quite porous and soaks paint into it so your not going to get bubbles. Always test on a spare piece of model plastic, preferably from the same kit. Second is are you priming your models? The paint will stick better when it has a primed surface to adhere to. Third is are you using a moisture trap? Compressors have alot of heat which causes moisture and that can get into your line and hence your paint if you dont have a trap. As the water evaporates it will cause bubbles to form in your finish. Try these few tips and see if you cant get it sorted out.