Both times I've seen someone apparently nicking a bike in the town centre and called the police, they have attended quickly enough to detain the possible thief (I can't figure out how to see the call length on my mobile phone's log, but I'm pretty sure it's within 3 minutes). I kept them in view from a safe distance until the police arrived. King's Lynn has officers on foot in the centre and on bike in the town - I'm surprised if Bristol doesn't. I suspect they're mainly intended to deal with public order, shoplifting and theft-from-parked-car offences.
I know they're not interested in everything (they were less than keen to come get an illegal mini-moto out in the villages), but what police would turn down a fairly easy catch of a bike thief in the act?
I waited 45 minutes for response to a 999 call once when I reported a burglary in progress, by the time plod had deigned to appear the goods had probably been sold 3 times over. I am not as optimistic as you are.