The English sentence is very odd, it is grammatically correct, though. You'd say cross the bridge, if you mean to walk on it to get to the other side.
Pass over, can be taken to mean fly or otherwise be over the bridge without necessarily being in contact with it.
As of June 2017, "It is dangerous to cross the bridge" is accepted, and I think that is what "É perigoso passar pela ponte" actually means.
Peter is correct that "It is dangerous to pass over the bridge" means something else. Therefore, it should be taken out as an accepted translation, although "It is dangerous to pass over on the bridge" or "... to pass through on the bridge" would have compatible meanings, if we wanted to stick to using "pass" as a verb.
I have also encountered the correction "It is dangerous to pass by the bridge", which would mean something different yet, and it also should not be accepted, if we are to learn this Portuguese sentence correctly.
This begs the question -- why we don't see "cruzar a ponte" in the Portuguese? It dawned on me -- because we are so used to the expression of "crossing" a bridge, we don't focus on how peculiar a way this is expressed in English. What we are crossing is not the bridge but something else, such as a river, a gully, or a (another) highway, rather in departure from normal uses of this verb. Once we recognize our own idiosyncrasy, then the Portuguese way of expressing this appears rather logical and ordinary.
Interestingly enough, "crossroads" (crossing) – cruzamento in Portuguese – obtained their name from religion (otherwise called intersections or junctions). Many of them would have chapels, or at least shrines:
Portugal is among them, and probably Brazil is too for that reason.
Like most of the ancient world, Romans believed that spirits gathered around crossroads. It was therefore common to find a small shrine, or compita, set up wherever paths or roads met. These would have four altars to honor the spirits in each direction.
I would bet this is also where the Portuguese word, Lar for home comes from.
Families also had a protective spirit, called a lar. Each family had a larium, or shrine, to this spirit, often kept in the atrium or courtyard. The head of the family – the paterfamilias – was responsible for making regular sacrifices to honor the family’s spirit and make sure that it continued to watch over them.
As for "bridges" that go over roads, I believe those are often called, overpasses (ironically called a flyover in the UK) while the roads below are called, underpasses.
I realise what you mean (although 'por' in this case would have to be translated to "over" if you want a preposition in English), but the case is that English doesn't need any preposition in this case (the verb and the noun acting as the objective in the sentence is sufficient if the subjective is actually passing over the bridge) whereas in PT you need to use a preposition. Whithout 'por', the sentence doesn't give a clear meaning. Hence "he's passing the bridge" should indeed be accepted (reported by me twice), and furthermore the suggested translation "he's passing BY the bridge" should be removed. The latter does not mean he is crossing the bridge. :-)
This is just how it is with prepositions in different languages, I'm afraid....any language has it's expressions with strange prep usage. In English we say "She's going to school" meaning she is attending school (as a general occupation) even though the verb + prep indicates she's walking there. In Norwegian we use the prep translating to "on" for the same...indicating she's walking on top of the school building... I'm afraid prepositions and expressions using them just have to be learned :-o