There are quite a few bus stops for the York City Sightseeing Bus along my normal morning bus route. The buses run all year round, have a running commentary, and you can get on and off as much as you like. Unfortunately I won't be reporting back about whether it's any good, because it costs £10 for a ticket, which only lasts 24 hours and seems to go where my normal bus goes anyway :-D
I buy a weekly ticket for the ordinary bus service, which costs £15 and with it I can travel anywhere on any bus within York. I intend to do some exploring some time soon.