City slumped to a second successive defeat after another lapse in defence allowed the Wycombe dangerman to head home from an acute angle after just seven minutes.
Wycombe's preparations were disrupted by a goalkeeping injury crisis, but emergency keeper Frank Fielding excelled as they secured a second away win of the season.
Blackburn loanee Fielding was an eleventh hour call-up by manager Paul Lambert and he repaid his faith with a couple of crucial saves, including a late stop to keep out a fierce Eddie Johnson free-kick.
While McGleish made the most of his early chance, City boss Stuart McCall will be frustrated that his side failed to make the most of several good openings.
Winger Omar Daley posed problems for Wycombe with his pace on the right, but too often his runs failed to have any end product and he was twice denied by new recruit Fielding.
City gifted three goals to Hereford in their defeat last weekend and they were guilty of sloppy marking again as McGleish headed a deep free-kick back across goal and into the net.
Bradford midfielder Paul Evans caused problems with his set pieces and striker Peter Thorne was inches away from a first goal of the season when the Welshman's 28th minute free-kick whizzed across goal.
City had several half-hearted penalty shouts waved away, but they had a let-off when McGleish got free in the box after 64 minutes and blazed over the bar.
McGleish fired a near post shot wide of the target with 15 minutes to go and five minutes later City survived another goalmouth scramble.
Fielding tipped away Johnson goal-bound free-kick with nine minutes to go, but the Bantams still had one last chance to snatch a point.
Striker Guylain Ndumbu-Nsungu flicked on the ball to send Thorne powering into the Wycombe box but, as he stumbled past his marker, the City frontman could only guide the ball wide of the goal with Fielding stranded.
The frustrated home fans had a couple of late shouts for penalties waved away by referee Rob Shoebridge, but Wycombe did just enough to hang on for the win.