They were indeed called trolley buses. I used the 215/6, Ashton bus, from Ashton New Rd, into Stevenson Square. I found them to be quiet, pollution free and good acceleration. I think the network ran until 1966.
Maynes bus company who had a garage in Clayton/Droylsden ran a convention bus down Ashton New Rd which we preferred as it was limited stop and was quicker to get in and out of town.
The 53 though was my lifeline, enabling me to get to school in Openshaw, then work in Crumpsall, as well as Maine Rd to watch City and Belle Vue amusement park for speedway. Coming back from watching City we would go upstairs where it was thick with cigarette smoke but nobody bothered then and if it was raining the windows were all misted up so you had to keep an eye out for your stop. The terminus was Queens Rd, Cheetham Hill the other Brooks Bar unless it was a 53x which might terminate at Belle Vue. As a child I always wondered what this Brooks Bar place was like.