Montamos a bicicletas doesnt mean anything. The expression is "montar EN bicicleta (in singular)". You can "montar a caballo" though.
"Montamos bicicletas" means "we assemble (or assembled) bicycles".
This sentence sounds odd to me as it is. I would say "Montamos en bicicleta el verano pasado".
when the verb montar is accompanied by the noun that designates the cavalry or the vehicle in which it is mounted, it is constructed as intransitive with a complement introduced by the preposition "en", or "a", if it is the noun horse: montar en coche, montar en bicicleta, montar a caballo".
This comment interested me, so I asked about the matter here.
Seems to me that, at least for those of us to whom "We rode the bicycles..." sounds somewhat unusual that "our" is the default option for capturing the meaning provided by the "las."
See for instance here how about half the translations for "ride our bikes" include some form of possessive, but half don't .
So "manejar" is just for car? We cannot "manejar" with bike? "Montamos" is for me from "montar". And "montar" can be both: "to ride" and "to put together". "Last summer, me and my friend worked in bike factory and assembled bikes".
Your statement has a similar meaning to Duo's statement but uses different words and would not be the same translation. Rode = montamos while went is fuimos.
It is best to stick with translating the words Duo gives you rather than composing a response using different words.