Financial websites and apps protect your information by encrypting it before sending it over a network. As a result, your information is quite secure, even if someone is listening. Your browser should notify you when you’re on a secure site by displaying a padlock icon and showing “https” (the “s” is the important part) in the address bar.
However, the appearance of a secure site is no guarantee. If you connect to a compromised network, hackers can redirect you to a fake “secure” site instead of a legitimate website. Even if you use a bookmark or type in the web address correctly, you can end up on an impostor page that looks just like a legitimate site.
Which will I suggest?
Use Private Window for your banking usage.
The main purpose of Private Window with Tor is to allow anonymity. The site being accessed can’t find out your IP address and anyone monitoring your traffic can’t tell what you are accessing.
Given that you are going to have to log in to the bank and they obviously will know it is you, the bank will be using SSL ((because protecting the integrity of the login form and/or other links and entry points into their authentication method are extremely vital) so your communications are encrypted all the time. Tor is to protect the identity of it’s users from the recipient of their requests, not to secure their connection for the duration of usage.
So banking with Tor is a big NO.
But what about public networks?
Don’t use it for banking purposes. If you have a data plan, use your mobile network instead of public WiFi for banking.
Use VPN when you are connecting to public networks.