The 20-year-old has been with the Black Cats since the age of eight, coming up through the academy and breaking into the development squad in 2013.
Since then, Beadling has been training with the first team and cemented his place in Andy Welsh's Under-21 side, going on to play in the EFL Trophy with the Under-23s this season.
Beadling posted on Twitter: "Very happy to have joined Bury FC on loan until the end of the season. Can't wait to get started."
The Shakers currently sit 21st in League One, two points from safety.