Yes, you can set up a bank account. The others are correct that you don't want to use a person's social security number. People have SSN, entities have EINs (Employer Identification Number). Getting an EIN is simple and free. You can handle it immediately
online with the IRS
.
The EIN has nothing to do with how big/small you are, if you have employees or not, or the type of organization (non profits, for profit). It's simply an identifying number assigned to entities.
Call around to local banks and ask what type of account they can offer with no fees/minimum fees and what paperwork they want.
For the last one I set up a couple weeks ago, I took my IRS paper showing EIN, minutes of our meeting showing officers, and a copy of our bylaws (which they never looked at.)