I am not a very big fan of the bank as a whole. Really bad customer service. One of the worst banks that I have encountered, but give credit where credit is due. The website is very secure. When you want to access the website, in addition to entering your location, user name and password they text message a one time use access code to your cell phone, that you have to enter in the site before it will allow you access. I like that idea. Very secure.
I am very conflicted over BofA. The site is safe, and among the most secure thanks to some recent changes in user-id and the use of multiple authenticating avenues. That said, I take umbrage with the way the company is run. If you don't know what I am talking about, Google it. That said I have no reason to think that your money is at risk or that your account is particularly vulnerable as a result of being associated with BofA.