Bradshaw netted in both halves in a 2-0 win, while on-loan 'keeper Saul Deeney kept a clean sheet in his first appearance for the Tigers.
Greg Strong completed 90 minutes in his return from an elbow injury, and Andy Holt, Mike Price, Lee Philpott, Scott Kerr and Nathan Peat were also on show.
City line-up (4-4-2): Deeney; Heard, Chapman, Strong, Holt; Price, Philpott (Fry 52), Kerr, Peat; Bradshaw, Donaldson.
Un-used subs: Russell, Crutwell, Turnbull, Wiseman.
Greg Strong completed 90 minutes in his return from an elbow injury, and Andy Holt, Mike Price, Lee Philpott, Scott Kerr and Nathan Peat were also on show.
City line-up (4-4-2): Deeney; Heard, Chapman, Strong, Holt; Price, Philpott (Fry 52), Kerr, Peat; Bradshaw, Donaldson.
Un-used subs: Russell, Crutwell, Turnbull, Wiseman.