I'm in a school that not only uses Bess, but also some other program (PC-cillin) that disables any actions to any file (excluding opening and closing them, of course) but then that kind of got me thinking. If it allows "gaps" in the "barrier" for those, wouldn't that allow someone some kind of access between the blocks. Unfortunatly all I have to offer is an analogy sense suggestion, (but as Adult Swim says, think of the possibilities!) but I also have more information in mind....
Sit infront of the computer as long as you can, trying possible passwords to get through Bess
Another idea, is how does Bess track a computer, or the network. If it's an individual computer, wouldn't a simple IP change be an option, but further more, a network, either fuck it up, and don't leave you're name anywhere, or best of wishes trying to bypass that (however you think you can O_o)