We painted a ceiling of an upstairs bedroom using high quality ceiling paint and many bubbles were formed when applying a second coat. The ceiling was previous painted.
What paint did you use? Manufacture and type? Most like problems occur when the second coat is applied too fast, the first coat wasn't fully dry, or there is a problem with the original painted surface. How much time passed between coats? Did you wash or prime before applying the new paint.
At this point lightly sanding to remove the bubbles and priming with a good universal acrylic primer should take care of the problem. After the primer has dried according to the instructions you can go ahead and apply a final coat.