I have a bag I specifically bought as a grab and go. It's small, for around town, but has harnesses, leads, treats, pick-up bags, bands, scrunchies, small brush, comb, and a doggy water bottle I fill before we leave, that live in it all the time. In the truck we keep a memory foam mat just for them. We put the mat into the bottom of the cart because twice Brody had a sore paw from being in a shopping cart. We have not left them anywhere yet, but I cannot imagine that I wouldn't be making up a much larger bag if they were going to be without me.
We puppysit a Shih Tzu who brings her kennel, brush, harness, lead, and food only now. Our friend knows we really only need the kennel sippy bottle because we have everything else and can hook the sippy bottle to the kennel that lives in our dining area! Plus, I always have some special little thing to send home with her again...usually some pretty hair bows, etc. I sent a pack of scrunchies home last Monday, and I've got darling hair embellishments I got for her as a surprise before Christmas last year...for another time.
Aren't they just so much fun?