A theory of mine is that after Dany "passes beneath the shadow", she'll learn that Asshai'i have traveled the Sunset Sea to Westeros, and that must be her path. Pretty sure there's a passage in the book about Asshai'i goods at the Shadow Tower, which strongly suggests it had to have come from the Sunset Sea. Because no Westerosi has traversed the Sunset Sea and told the tale, I quite like the Dragon invading from it