The home side created the majority of the chances but rarely troubled Matt Duke in the Bantams' goal.
Cheltenham defender Steve Elliott put a header wide from eight yards after 16 minutes before Byron Harrison sent a header into the hoardings seconds later. Duke then pushed away Pack's long-range free-kick.
A red card for Bradford's Andrew Davies with an hour played, for a second booking - meaning he will miss out on his side's opening play-off game - gave the Robins a one-man advantage but they could still not find the breakthrough, skipper Russ Penn's searing 20-yard drive over the crossbar the closest they came.
Bradford finally managed an effort on goal in the 77th minute but Nathan Doyle's effort was wide of Scott Brown's goal.
Normal service was resumed as Cheltenham finished the stronger with Pack heading against the post from a corner and substitute Shaun Harrad forcing Duke into a decent save five minutes from time.