I'd either turn it in to the police or put up posters, saying:
Found:
Bag. Has a phone, money, make-up, etc.
If you have lost it, please call to collect it.
Then there's the whole, "ZOMG, DAT'Z MINE." Fiasco. I'd ask them over the phone, for some information about the bag. They get it wrong, I say, "Sorry but this isn't your bag." Get it right and I'd arrange a place to collect it.