BanReservas (or banco de reservas) is the easiest to deal with. i have a USD account with them and all that was needed to open it was my passport. Banco Popular wanted million other things. the way the process works is simple, you tell them you want a USD account, they take a copy of your passport and send it to Santo Domingo to investigate if you have any criminal record, i was told they also contact your embassy to check your record, i was told the reason was to fight money-laundering. the whole process takes about two weeks, they'll tell you they'll call you back but you have to follow up yourself, if everything is OK they open the account and you're in business.