JoAnn,
I have run into this problem as well and heres what has worked for me:
1. Put the inclusion into your project slowly. What I mean by that is to let it sink on its own, then position it. I dont know what the physics behind that is, but it seems that air bubbles will trap next to the piece if you force it into the resin.
2. If your inclusion is flat (paper or something similar), put it in your resin on a 45 degree angle and get it in completely before positioning. If you put it on top of the resin while flat, then push it down, you will definitely trap bubbles.
3. Are you working with clear/semi opaque molds? If so, there is nothing stopping you from picking up the mold carefully and looking underneath to see if there are any trapped bubbles. If so, move your inclusions around or tap them with a toothpick to release the bubbles.
Let me know what you try!