Anton Forrester's strike allowed the Shakers to jump above their rivals into 20th in League Two, two points clear of the drop zone.
Bury outlined their intention to attack early on, Forrester and Andrew Tutte both going close with long-range efforts.
The hosts bagged the only goal of the game in the 34th minute, Forrester finishing a swift counter-attack by turning sharply to hammer into the bottom corner.
Wycombe tried to respond but Scowen fired into the side-netting from a Reece Styche cross.
And another free-kick right on the edge of the box was wasted when Nick Arnold hit the wall.
Chances were more restricted after the break but Ashley Grimes fired into the side-netting after finding space in the penalty area.
A last-gasp block denied Forrester a second while Nick Arnold volleyed narrowly wide of a post.
- Sports & Recreation
- Anton Forrester
- Josh Scowen
- Andrew Tutte