I normally carry a one strap, messenger style bag when I ride (anything). The preferred ones I like have a grab handle on the top / back side and I can carry books, camera, tripod, sunglasses, sandwich, water etc.
I never leave it on the scooter when going in someplace, and will even move it out of the way, when I'm gassing up. I look at my P 250 as a two wheeled pick up truck and have hauled 2 forty pound bags of birdseed home and got caught by the police when I was moving two one gallon pots with four foot tall decorative grasses on the floor boards.
When the cop asked me what in the he<< I thought I was doing ... I told him I was in "Stealth Mode" and he shouldn't have been able to notice me. I had the messenger bag in front of the plants. His eyes kind of glazed over and he just muttered to himself when he walked away.
It pays to be gray haired when you ride two wheels. They always expect to find a kid on a bike - of any kind.