If I understand correctly, you're saying that you will drift as you move toward the other bank.
If you find the y-component of your velocity then you're finding your northward velocity (irrelevant to the downstream (eastward) movement in this question).
To find the time to travel between both banks you could just find the y-component of the velocity and divide the distance between both banks by the result. Then using that time and the sum of both x-components, find the distance traveled downstream.