What ToR does is route your internet traffic through a network of random computers all over the internet to make it harder to trace your actions back to yourself. It is commonly used for nefarious purposes or by people who want the illusion of privacy.
Your connection to your bank is almost always (unless we are talking about a totally incompetent bank) going to use SSL encryption (https://) - This means that your data is encrypted end to end, from when it leaves your PC to when it reaches the bank's computers - Your ISP cannot read this data, all they can see is that you are sending encrypted data to the bank. With online banking, your account is extremely unlikely to be compromised over the network, if anything you would have your login details collected if you had a virus on your computer.
If I'm honest, using ToR for "privacy" or "security" is a bit silly, all it does is first of all route traffic through random people's computers (which IMO could actually make your data less secure), it has already been seen that some nodes on the ToR network have either been compromised or are run by the NSA. And in the end, if you are trying to stay away from any sort of surveillance, using ToR shows that you are possibly up to no good.
Michael also makes a very interesting point, Bank's websites are often built to lock accounts that are suspected to be under attack, if you connect using ToR and are therefore detected as connecting from different countries all around the world, this could well be enough to lock you out.