Foreign Citizen forming a DBA / Sole Proprietorship
Technically speaking, yes you could register a DBA as an international resident, being that you could use your social security number to obtain an EIN.
To register a DBA in the United States, you would need to have a business address in the state you are registering in. In many states, DBA's are filed with the county or town the business address is in, and the application will require you to sign it in front of a notary public, often licensed by that state. This could make registering a DBA a little more difficult than registering an LLC or a Corporation in your circumstance of living outside of the country.
As DBA's are registered differently state to state and sometimes county to county, it is hard to give an accurate cost estimation.