they make some interesting "bag locks" for luggage and the like. If, as you say, you're in a monopoly, and you can't get away with shopping with the bag, this might be some peace of mind.
This is currently why I don't participate in the weekly special at a pizza pub my friends love to go to. Its on campus and they've had issues with backpack-wearers (whether student or not i leave to speculation) stealing pint glasses. I respect their rule, but I have to bring a backpack on my weekly commute. I've thought of asking the manager if I could arrange to bring it on the condition the he provides storage or an entry/exit search. I'd be a bigger fan of a search since I carry a laptop.
Of course I'm probably better off not biking after a pitcher, and nobody's trunk is big enough to fit my bike