Bearman's lineout catch and pass created sufficient space for Thomas to crash over and Arlidge's conversion and penalty slashed the interval deficit to just six points.
Giteau's conversion made it 10-0 at the interval, James landing the hosts' first points on the resumption - and their first in 125 minutes of Test rugby - before giving way to Francois Steyn at fly-half after 55 minutes.
Henry Paul, who switched to full-back following injury to Justin Brooker, kicked his second conversion to give Bradford a deserved eight-point interval lead.