It's probably not too wise to ride around for extended periods of time without a few essentials; air pump, pressure gauge, lock, printed copy of local regulations, pen, paper, sun screen and maybe a sweater for when the ride turns a bit cold.
I don't think I can recommend the
Segway Handlebar Bag as a replacement for a briefcase, but for holding stuff you probably want to have access to every time you ride, it's not all that bad.