According to the académie française, en vélo is incorrect. The preposition en is reserved for means of transportation one can get into, like a train, a car or a bus. But other linguists hold the opinion that en may well be used with a bike because it doesn't mean so much "in" as "by".

Here is an interesting article: https://www.lefigaro.fr/langue-francaise/actu-des-mots/2018/06/03/37002-20180603ARTFIG00008-j-y-vais-a-ou-en-velo-ne-faites-plus-la-faute.php

All these ruminations would also apply to a bicyclette, I'm sure.