It was visitors Birmingham who went in front through a Tommy Taylor try, their opponents hitting back as Chris Smith crossed before Chris Bolton added the extras.
A Taylor penalty nudged Moseley back in front, only for Alex Gilham to dot down for 12-8 Stortford.
The lead changed hands twice more before the break, Taylor on target after Tom Miles touched down before Declan Murphy put Bishop’s back in front.
Mike Cooke converted an Austin Pope try on 50 minutes to push the hosts 24-15 up, but Birmingham replied swiftly via Ollie Allsopp and the boot of Taylor.
Gilham received his marching orders in the final quarter, but Cooke landed after Will Rogers crossed to mean Ben Pgoson’s late score, converted by Jack Jolly, was not enough for the visitors.
