Oregon Health Plan covers transgender stuff. It's pretty low down on their list of priorities, but they make a point of considering it necessary and not cosmetic.
Anyway, on Oregon medicaid testosterone is free if you get the shot at the doctor's office instead of doing it yourself. The appointments with the physician are covered, and the labwork is covered. It's going to get billed as what it is (liver panel, cbc, hormone levels, etc), and doesn't have TRANS stamped all over it. It is decidedly a grey area to operate in though.
That's probably not helpful though, as I don't know much about Washington.