"We descend from the bridge into the city."
Translation:De ponte in urbem descendimus.
You could say that; it might suggest, though, that you were on the way to the city, whereas "in urbem" seems to insist on the winding up inside the city.
In my opinion, this would have more importance if the verb were in the past tense: i.e., whether we went towards the city (ad urbem), versus going all the way into it (in urbem), would be more of an issue. (If it were in the past, then we could say that it had happened one way or the other.)
As you say, since the verb ending indicates the subject (-mus = "we", -tis = "you, pl."), there's no need for the subject pronouns (nōs and vōs ), unless they are being emphasized.
(This goes for all the subject pronouns: ego and tū , as well as the 3rd person pronouns, such as is, ea, id or ille, illa, illud , etc.)
The emphasis usually comes in, when you're contrasting what two different subjects are doing (Nōs labōrāmus; cūr tū nihil facis ? = "WE are working; why are YOU doing nothing?"), or if you have some other contrast in mind:
Nōs eōs miserōs iuvāmus = "WE are helping those poor people."