Wanderers: Ingram, McCoy, Mustoe (Cowan-Hall 71), Doherty, Johnson (Stewart 54), Arnold, Scowen, Lewis (c), Wood, Styche, McClure (Jeffrey 87).
Despite enjoying more territorial advantage, the closest the Chairboys came to a late leveller was when Mills headed onto the roof of his own net.
The 23-year-old saw his delivery poked wide by Arnold, who then sent a volley narrowly past Jensen’s right-hand post with 15 minutes remaining.
Anthony Stewart replaced the injured Leon Johnson before Jordan Mustoe made way for Cowan-Hall, who injected a bit of life into the visitors as they looked for the equaliser.
Matt McClure mis-hit Wood’s inviting cross from the left while, at the other end, Ashley Grimes hit the side-netting with a close-range effort after bursting into the Blues’ box.
Nick Arnold then forced Jensen into a save from distance as Wycombe ended the half on top, which they carried on into the opening exchanges of the second period.
The Chairboys responded well to going behind and almost drew level instantly, but Josh Scowen wasn’t able to turn Reece Styche’s cross home from a tight angle.
Forrester didn’t miss with his next opportunity though, firing low under Matt Ingram into the bottom left-hand corner from the edge of the box on 34 minutes.
Despite the visitors’ two half-chances, it was David Flitcroft’s men who were enjoying the better of the ball and they nearly turned that possession into a goal midway through the first half, but Forrester’s dipping volley went inches wide of the target.
Another poor pass, this time by Pablo Mills on the edge of Bury’s 18-yard box, presented Sam Wood with a shooting opportunity, but the midfielder saw his effort blocked.
Wycombe’s skipper Stuart Lewis registered the first shot on target when he tested former Burnley keeper Brian Jensen after the hosts squandered possession 30 yards out.
Gareth Ainsworth named an unchanged team for the third consecutive fixture, while Paris Cowan-Hall was back on the bench following a knee medial ligament injury at the expense of Kortney Hause, who joined Wolves on Friday.
In a closely-fought encounter, the game was decided 10 minutes before the break courtesy of a strike from Shakers striker Anton Forrester.