What is the best board to install behind a glue up tub surround?
Most use standard drywall. If you feel better using dens shield or another WP drywall that would be fine tub surround adhesive must be used to avoid discoloring bleed through on the surround. Two adhesive makers indicate they will work well. Honestly if they will bond to ceramic tile they will bond to most anything. 

From the manufacturer:


  Liquid Nails LN715-10oz Tub Surround and Shower Wall Adhesive is a durable construction adhesive that provides an exceptional waterproof bond under extreme conditions. LN715 Tub Surround and Shower Wall is recommended for bonding most plastic and fiberglass tub and shower surrounds to drywall, plywood, greenboard, cement backerboard, and ceramic tiles


And another manufacturer 


  Loctite PowerGrab 10 fl. oz. Tub Surround Adhesive with low odor, low VOC and easy water cleanup is an ideal interior construction adhesive. It is designed to bond most plastic surround tubs to waterproof drywall, wood, sanded tile board and ceramic tile.