I have to agree with Eric 100%.
I have had jobs where surfing the internet was strictly forbidden. Hell I worked for America Online back in the day and even THEY would get pissed if you were on anything than an AOL site.
What it come down to is you're there to work, not play. I can understand where your coming from Score, it sucks being at work with nothing to do to pass the time when things are slow. What I would do, is ask the boss if there is anything you can do on your downtime, even if it's something you don't want to do. I know you said that working at a bank isn't what you want to do for the rest of your life, but when you're going for the job you want and need them as a professional reference, do you want then to say you were an asset? Or that you seemed like you were only there for a paycheck?
Who knows, if you show initiative, more doors might open for you like they did for Eric........