I agree with Joe, having the money deposited to the US bank account may land you in trouble. Technically, a US business paying a foreigner must withhold 30% of the payment, unless a tax treaty says otherwise. The US business should do that based on your W8-BEN/W8-ECI form that you should have given to the business before being paid.
I'm guessing, that by paying to your US bank account, you (and your American counterpart) are trying to avoid this withholding. That may cause trouble for both of you. I would suggest you talking to a professional (EA/CPA licensed in the State where the business is located) and having the situation resolved ASAP.
You may not be liable for the US taxes at all, but because of incorrectly reporting the income/expense - you and the US business may end up paying way more than the $0 you otherwise would have, in penalties.