If you can't convert your bitcoin into fiat, then your only option is to use your btcs to purchase goods and services directly, which would further disincentivize businesses from accepting bitcoin as a form of payment. And if you can't send fiat to an exchange, you can't increase your holdings.
This would require you to open a foreign bank account, which you must tell the U.S. government about. Not telling them is a serious crime. See the Foreign Account Tax Compliance Act