The Sky Blues lost Colin Hawkins early on to injury and had Liam Francis taken off with a broken nose after a clash of heads.
Chilean Willy Top scored the only goal of the game just before half-time and Wayne Andrews hit the bar in the second half whilst Danny Ireland made three good saves.
David McNamee was the replacement for Francis and came through twenty five minutes unscathed.
City: Ireland, Robinson, Francis (McNamee 65), Hildreth, Hawkins (Burgess 7), Turner, Burtoft, Fitzharris, Simmonds, Andrews, Davis. SNU Walker, Grandison, Ashraf.
Bradford: Saynor, Morgan, O'Brien, Bentham (Griffiths), Hopkins, Ainge (Smith), Penford, Topp (Osbourne 46), Joynes, Medley, Taylforth. SNU Convey,Sharry.