When you have sanded, be sure to clean the surface with a tack rag right before you apply the next coat of poly. Any sanding "fuzzies" seem to make more bubbles.
Too late now, but with oil based poly, I thin the first coat a bit, then thicker for the second coat and then "from the can" strength for the last coat. This makes it less succeptible to bubbles and they "pop" faster on the rougher surface of sanded wood. That good brush is a good answer for most applications but doing it this way, I do use a foam brush with no problems. I don't do enough with water based poly to comment.