First, the geography of the area was very different in antiquity. Everything I've read has suggested that the Hellespont (Dardanelles) had much more narrow spots in the 6th century BCE. I don't have any sources for that on hand, but searching for "Hellespont geomorphology" or the like will produce something.

Second, Darius I in fact did cross at the Bosphorus on his campaign against the Scythians in 513 BCE. When Xerxes I crossed over into Europe during the Persian Wars, it was his route that determined the point of crossing. He was moving north from Sardis, and the Bosphorus crossing would have been a more circuitous route.

Speculation mode: I don't know about previous crossings by any group, but if indeed the Hellespont had never been bridged previously, it is feasible that Xerxes choose to cross there for the "did it first" value. He was not a humble man, to say the least.