Reay was on hand to convert a Lewis Walby pass in the 26th minute after Jordan Cullinane-Liburd had put the Bulls ahead.
Simeon Maye - who has signed for Hereford after impressing in trial - swung over a corner in the 11th minute, which Cullinane-Liburd swept home.
After equalising, Bideford had a chance to go ahead moments later, but Billy Tucker's free kick was pushed onto the bar by Hereford keeper Brandon Hall.