Bank of America is one of the largest banks in the US, but as of today, you can't do any banking with the company via your Windows Phone. In late January, the company announced that it was pulling support for its Windows Phone app, but the app still worked, although with a message urging users to use the web interface instead.
Opening the app now gives you an error, stating:
We no longer support the app and you may not have browser access to bankofamerica.com for this device.
But you can access Online Banking through your laptop or desktop browser or a mobile device with a supported operating system. Just go to bankofamerica.com for a list of supported browsers and operating systems.
And indeed, Windows Phone users appear to be unable to get past the sign-in page at bankofamerica.com with the built-in IE browser, and so are essentially locked out of using Bank of America's services via a Windows Phone at all.
Chase Bank also recently announced that they would no longer be supporting Windows Phone, although they recently stated in a forum post that the app would continue to work for the time being. Wells Fargo, another large US bank, announced it has no plans to pull Windows Phone support.