godan verb (-su), transitive verb
spin vigorously; wave around
Colloquial transitive verb for swinging or spinning something forcefully and often wildly, such as a bat, sword, or steering wheel.
バットをぶん回してホームランを狙う。
He swings the bat hard, aiming for a home run.
ハンドルを思い切りぶん回した。
I spun the steering wheel with all my might.
振り回す is a more standard word for waving or brandishing something, while ぶん回す is more colloquial and emphasizes forceful, vigorous spinning or swinging.
The prefix ぶん- adds emphasis or forcefulness to the verb 回す (to turn/spin). The exact origin of ぶん- is uncertain, but it appears in other colloquial verbs like ぶん殴る (to punch hard).