You have the rough idea. If you google a bit, you should find
installation instructions from the manufactures of vinyl sheet
flooring, which covers this problem.
I just installed some vinyl flooring, and the instructions that came on
the can of adhesive detailed this (sorry, now in the trash) procedure,
and so did the installation brochure I think.
Small bubbles just needed a little cut to let the air out. Larger
bubbles you could inject some adhesive, but I don't remember the
technique. There is (I think) also a sealant that you can paint over
the cut to seal it back up. Again, covered in the instructions.