A well-worked move 5 minutes into the second half saw City double their lead. Whitmore squared the ball across, and Bradshaw dummied for Rob Matthews to shoot past the Town 'keeper with his left foot.
Paul Aldridge pulled one back 10 minutes later, before Richard Tracey beat Matt Glennon in the 75th minute to level the scores, and 2-2 is how it finished.
Neil Mann completed 90 minutes after returning from a hamstring injury, while trialist forward Dean Cropper was also in the starting line-up.
The Reserves are next in action a week today as they travel to Rochdale. The game at Kidderminster looks set to be postponed for a second time due to other commitments.
Starting line-up (4-4-2): Glennon; Morley, Bloomer, Mohan, Price; Matthews, Petty, Whitmore, Mann; Cropper (Dixon), Bradshaw.
Un-used subs: Peat, Kaveney, Mulchinock, Bowsley.