Don't access your account from a public computer or a PC used by several people. If you do, don't keep your ID or password stored in memory, always log off the service once you are done and dump the browser cache after every use. If you surf to another site for a few minutes without logging off, a secure service will require you to log in again when you try to return. To be extra careful, you might also check the site's imbedded security certificate each time you log on to be sure it's in order. If you aren't willing to trust your bank's data protection measures or the encryption technology it uses, there's no point even signing up.
Peace of mind is worth more than convenience.