Does your agency not have a jump bag they take in on calls? Thats where all my bandaging supplies and PPE have been. I do carry a few pairs of rolled gloves in the ankle pocket of my pants, protocol book, scissors, a pen and a marker in my side pocket. Not sure what else you'd need to carry on your person vs in the bag.
I've seen a couple people with fanny packs, but they were never approved by the company. They carried items that were included in our drug box, but so they could just bring their pack instead of the big tackle box we used as a drug box, if they were feeling lazy. Also sometimes carried items our company wouldn't stock, so we "borrowed" from the hospitals. Usually had a work up kit, zofran, ASA, nitro, a few syringes, high pressure IV tubing, a pediatric pulse ox, can't think of what else. I'd be careful with carrying a pack like that though, as many of these items you shouldn't be keeping with you away from work.
Sorry I can't be more helpful, best guess is to just ask the other people at your service what they carry.