Being the bored language nerd I am, I just looked it up in a couple of places...

Montar is the more frequent in what I found (mostly European sources) so I'm leaning towards the Spain vs LAm theory. (Looked at wikipedia, the elmundo dictionary, merriam webster and a couple of other dictionaries plus a search among el País articles and elsewhere on the net. The oxford Sp dict and a couple of other sources actually have "ir").

I'll ask Cristina... unless I forget to.

BTW: yeah, "bici" is often used just like "bike"... and pista is the default term for bike track. Perhaps not in Costa Rica but definitely in Spain and a bunch of LAm countries.