The London Transport bus seen in the film is a fictional fleet number LT1097 with registration KLB713, supposedly a prewar bus.
It was played by three separate postwar AEC RTs, RT1591 (genuinely registered KLB713, and deroofed for the film), RT 2553 (LYF278) and RT4628 (NXP881). London Transport's LT class were AEC Renowns rather than Regents; perhaps the most obvious difference was the two axles at the back of an LT as opposed to one on an RT!
Rachel Weisz refrains from spitting:
....while Brendan Fraser avoids standing upstairs:
The whole film shows an endearing disregard for historical accuracy. Filming was at Shepperton Studios. London Omnibus Engineering Services were responsible for the bus filming. Information is from British-Buses-Abroad-in-North-America discussion group, posted by Lionel Moss and Bob Martin et al. RT1591 previously appeared painted silver in the music video 'Go Let It Out' by Oasis.
The capture below shows RT1591; the capture above left is definitely a different bus (look at the white stripe across the front, and the offside sidelight) - I can't be sure about the shot above right.