Gmail is definately not the cause of your 250-300mb bandwidth usage a day. I use my Gmail Web Interface aswell as Pop3 it. I would say that on ave, you looking at around 20-30mb trafic for the day that wound be like 25 emails sitting at 1mb big each or the same with 200-300 text based emails. To actually check mail, uses just about nothing. The gmail web interface is well designed and only refreshes certain sections of the page. web cache also plays an important roll in this. When you open a mail and later open the same mail, it will open from cache instead of using new bandwidth to open that doc or text you viewing again.
A good way to check what apps is running, if any unwanted programs running in the background, is to check your CPU time. Im not to clued up with ubuntu, but try console command "top", that should show you your CPU traffic aswell as what processes running. You can also try ip traffic monitoring using console command "iptraff" to monitor network status (bandwidth being used). These commands come from Debian Sarge (linux), so dont know if they'll work.
Good Luck Thou