Are you like talking about a jumpbag that you keep in your car for emergencies? Or a bag that you take in with you to work that has personal equipment?
As far as jumpbag, I just keep a small first aid kit for myself and anyone around me. You're much, much more likely to be treating a friend/family member than a random stranger. Just things in a standard first aid kit--bandaids, gauze, etc. I try not to keep like neosporin or meds in it b/c idk how they handle in the summer heat.
As far as a personal bag I take in with me, it has my stethoscope, a penlight, and a "tactical" flashlight. My knife is already on my person as are my wallet, keys, phone, and headphones (for the ride back if we transport--some hospitals are over an hour away!). If I'm not wearing it, I also keep a hat in there so if I'm not in uniform and responding to a backup run, when I inevitably transport and get to the hospital, I don't look like I'm a random guy trying to go in the ambulance entrance past security!
Some people also keep trauma shears and a towel in their bag, but the truck has trauma shears and towels and there are towels all over our station so I don't feel the need to bring a personal one.
Everything in my personal bag fits in a little drawstring athletic bag that can go on my back--you know the kind i'm talking about that you might take with you to the gym if you're already changed into workout clothes.