I was talking to our community officer for our school - who also does bike patrol. He told me that it was a option to do bike patrol, and that he could have chosen foot or cruiser if he preferred. Apparently one of the main advantages of the bikes is to run down people on foot - the front suspension/hardtail combo is useful for going down/up short flights of stairs.

AFAIK they are mostly community officers rather than traffic patrol. I think it's only the mounted patrol that they have to apply for, foot, bike or car are options that they are free to choose from - if you want to be on horse, you have to be approved for it...