When I did open a bank account like ten years ago, I have been requested to provide all the papers you have read in Dolores's link. In addition I had to find two witnesses pretending they knew me. This was at el banco de reservas the governement bank.
Pascal
When I opened my account at Banco Popular 5 years ago they wanted to see only my passport and my money!!
I did come in with someone (another foreigner) who knew the manager. I had been in the country for about 3 days; we entered his address, which we had wrong. I went to see the manager again to correct the address and he looked at me, saying like "what the heck do I care ?..."
All that u need is an ID .. Doesn't matter if it is a foreign passaport and money.. Now if u are interested in getting a credit card from a bank here in DR then it is a different story. In that case u will need someone to cosign for the application. That is all if u do not have a cedula ( dominican social security card- basically), if u have a cedula then you may go on ur own and they will need proof of income.