If you look at Xerxes' route, the answer is obvious:
Source: Map showing the Greek world during the Greco-Persian Wars (ca. 500–479 BC).
Xerxes' army moved North from Sardis, seeking alliances with or conquering Ionian cities. There was extremely little of interest for Xerxes after Abydos (the crossing point, according to Herodotus). Going all the way to Bosphorus, a few days of marching essentially in the opposite direction of Greece, just to save a few meters of a (floating) bridge wouldn't have been the wisest of decisions.
More importantly, Xerxes' land route was paralleled by the route of his fleet. The fleet was essential in the crossing:
- It provided protection from attacks from the Aegean,
- The bridge was actually a series of anchored ships.
Furthermore, had Xerxes' chosen Bosphorus, he wouldn't have avoided Hellespontus' turbulent waters, quite the opposite. The fleet would have had to deal with Hellespontus' unwelcoming waters twice: Once going from the Aegean to Bosphorus to support the construction of the bridge, and once returning.