I dug up the actual paper (Cook, 2004) and it turns out the bicycle was symmetrical... and, in fact, entirely virtual.

It's a plot of a computer simulation, rather than records from a real-world physical experiment.

A bicycle is composed of four rigid bodies: the two wheels, the frame, the front fork (the steering column). Each adjacent pair of parts is connected with a joint that allows rotation along a defined axis, and the wheels are connected to the ground by requiring that their lowest point must have zero height and no horizontal motion (no sliding).

So the simulation has a lot of simplifications from reality, and the picture tells us more about the simulation model than it tells us about the real world. It is a pretty picture, though.

Here's the paper reference:

Cook, M. 2004. It takes two neurons to ride a bicycle.

(I couldn't get it from the Cook's Caltech site, but I found a copy elsewhere.)