Drury's original loan deal from Leeds expired after last Saturday's match with Oldham Athletic, but the defender will now stay with Phil Parkinson's squad until after City's final game of the season at Tranmere Rovers (3 May 2014).
The 35 year old, who made his Bradford debut as a second half sub at Brentford early last month, has played seven games so far for Parkinson's men.
Subject to receiving the relevant clearances from The F.A and the Football League, Drury will now be in contention for a place in City's squad for this Friday's match at Rotherham United.