Yes, from a carrying bike points of view, the elevators are also fairly small iirc, you would probably have to hoik a bicycle into an upright position to fit in.
I think I'd just carry a bike up/down the stairs, it would probably be easier.
The station entrance/exit is at ground level.
I've never taken a bike through Wimbedon, since I mostly transit from the tube to the tram, and they won't let me take a bicycle on the tram.