Have you sealed the paper?
I actually don't have much experience with this, but paper is porous and can hold air, so if you put glue on top of it the air might form bubbles.
If you haven't already, I would try sealing the paper with mod-podge or something similar, use thin coats, let dry, and repeat. Then use a glue to attach the glass circle.
I have heard people mention that they use clear packing tape over their paper/images before glueing to a piece of glass or applying resin, you could try that as well.