Any bag will do!! Anything big enough to hold your purse, water bottle, a few nappies, bunny rug, (bottles if FF)
I stressed and stresseed over which bag to buy, and then I got given a normal handbag, not even very big, and it's got plenty of space even with everything in it! I'm pretty sure the bag cost $15, and when it breaks, I'll just buy another $15 bag.