I put the first coat of polyurethane on some oak plywood shelves last night, and it turned out horrible. The surface has a bunch of little tiny rough bumps...

Oil based poly, especially the typical brands at the big box stores, is way too thick to be applied by brush by most of us mere mortals. And stretching the finish over a larger area in order to obtain a thin coat exacerbates the problem even more. It is just too thick to level on its own if you over work it even slightly.

Even though the can will likely tell you not to thin it, thinning with mineral spirits or naphtha even 10% by volume will vastly improve its ability to level on its own. Naphtha flashes off faster giving the film less time to collect dust nibs, one cause of the bumps you talk about.

Poly on the first two coats does feel bumpy but the more coats with proper treatment between coats will be very smooth.