Bustitution drivers don't seem to have the same can't-do attitude as normal bus drivers, though it's been yonks since I had to use one.
As for normal buses, I certainly wouldn't rate your chances in Stockport. I wouldn't even try to take one on a Birmingham bus, and I'm not even black. Might work better in the People's Republic or That London if it's not too busy.
Of course for me one of the best things about having a bike is that you don't need to use a bus, but YMMV.
Anyway, assuming that hurdle's overcome, a Brompton wouldn't be high on my list of bikes that are fun to ride 100km on, and you really want bigger wheels for the COR...