How do I fix bubbles in the veneer of an antique table top?

If they are just air bubbles you can can cut a slit in the bubbles with an X-ACTO Knife and work some glue into them. Put a piece of waxed paper on top, and then something heavy until the glue dries. If, however, the table is made of particle board and it’s swelled up in spots there’s not much you can do except (perhaps) sand it smooth and paint it.

HI Melanie. Unfortunately once veneer has bubbled it is really difficult to smooth it out again. It means that the wood has warped so trying to get it to restick will take getting some glue under the bubble and clamping it until it is completely dry. Alternatively, you can try sanding it down until the bubble is gone and it is smooth and then fill the area and paint the piece. Here are some directions on how to do that... http://www.recreateddesigns.com/2016/03/fixing-veneer-easy-way/ Hope it helps!

If they are really antiques, try ironing the bubbles out, using a slightly damp (not wet) cloth, at a reasonably low temperature. Just don't let it get hot enough to burn the wood. Hide glue will melt and 'restick'. I once bought an old bamboo bookcase that was so nasty I had to remove the shelves and put the frame in the shower to get it clean. When it dried, the glue had reset, and it was as solid as a rock!

https://dengarden.com/home-improvement/Laminated-Wood-Veneer-Home-Repairs-for-Bubbled-or-Loose-Veneer-video