My understanding from my rebbi is as follows:
Riding a bicycle is uvda d’chol according to many poskim. The reason it is uvda d’chol is because the typical use of bicycle involves occasional melocha (fixing the chain) or issur (going out of the techum). Activities which can be done without melocha or issue but are typically done in ways that include melocha or issur are forbidden on Shabbos as uvda d’chol. This is not a new gezeira but simply the application of parameters of uvdin d’chol.