1) The "Which Direction?" discussion has been going on since 1492.
2) Although surface winds roughly even out over the course of a cross-country bike tour,
there is a slight advantage with a west-to-east trip - especially, because of a few regions with serious, prevailing west winds.
For ex. -
Rawlins, Wyoming on the TransAm has strong, southwesterlies all summer.
Havre, Montana on the Northern Tier has moderate westerlies in the daytime with return easterly flow in the early morning hours.
Hood River, Oregon on the Lewis & Clark has moderate westerlies all summer - thus, the wind surfers on the river.