I'm not sure what you mean by "pulling", Dr. A. The bike was behind you? Were you holding onto the handlebars and walking the bike to the shop?
If it were a car, that pulling would be called "towing." A bike won't stand on its own, though, so someone has to be holding it up. I think the most common phrase would be "walking the bike" - "I had to walk the bike all the way to the mechanic's shop."
To take it, though, could mean to put it in the back of your car or truck and drive to the mechanic's shop. If I take my son's bike in for repairs, that's exactly what it means - I drive it there in the car.
Did you carry the bicycle, Dr. A? I just thought of that. Was the bicycle rolling on its own wheels or was it up off the ground? I assumed it was rolling on its own wheels.