Yes, you can set up a Roth IRA at a bank, but IMO, your choices are very limited, and in my case, fees were extremely high. Two years ago, I opened an account with Fidelity instead, and I have been very pleased with their services. I believe that they require a minimum of $2500 to open an account, but after that, you're golden. No annual fees and a flat $19.95 to trade stocks. I reinvest all of my dividends for free as well. The money that is in the Fidelity account, but not in stocks, goes into a money market account, currently earning around 4.5%-5%. Their research tools are fairly extensive and free for your use as a customer.
Bottom line: I would review the myriad of choices available online and pick the service that works best for you. I do 3-4 trades/year, and Fidelity suits me fine for my needs. If you are a more active trader, there may be a company more tailored to your needs.