I would say it depends on a few things - how fancy do you want to get, how much space in the cruiser do you have, your level of training, and how long on average until the ambulance arrives?
One ambulance I used to work for kept large shaving kit bags on the head of the stretcher that could handle a lot of calls - stocked with exam gloves, scissors, pocket mask, tourniquet, BP kit and stethoscope, oral and nasal airways, some 4x4 and 5x9 dressings and roller gauze, maybe a small bottle of sterile water or saline, and a couple of triangular bandages. That list can cover a lot of things and doesn't take up too much room. Presumably you already are carrying a small notepad just to jot down name, date of birth and whatever vitals or other pertinent info you have to pass to the EMS crew.
It's easy to go all out and accumulate a mega duffle filled with all sorts of stuff, but the truth is, even working full time as a medic, most of my stuff is there for "just in case." We have to carry OB kits and tractions splints, things that get used maybe once every 5-6 years, if that.