Pista here in Costa Rica would mean you like riding on the main roads - as in Autopista. So a roadie would say, me gusta andar mi bici de pista.

Another term for track might be Carril - as in lane but I don't know enough about your sport to tell you if that would be correct.

If track means a single lane - then me gusta andar mi bici de carril might be correct.

Oh, and I don't think montar is correct. That generally means something where you sit and it does the work - like a horse for example.