The total length of the Bosphorus bridge is 1560 m [1]. The total length of the proposed bridge over Hellespont is 2196 m [2]. Even if there's a point on the Hellespont where the distance between the two sides is shorter than the shortest distance between the Bosphorus, considering the turbulent waters of the Hellespont, why didn't Xerxes chose Bosphorus over Hellespont to make the crossing?
As a side remark, I have heard the references to Hellespont far more often compared to Bosphorus, a fact which I find interesting.
References:
1. https://en.wikipedia.org/wiki/Bosphorus_Bridge
2. http://www.botek.info/detay_motor_12.html