Good on you for helping out.

Sounds like you have a good enough kit. My own is along these lines:

Good kit - A couple pairs of nitrile gloves, sterile non-stick gauze pads (4"x4" would be the largest I'd carry), some hypafix (one of my favourite if not my very favourite small wound dressing product), an assortment of band-aids, tensor bandage, sling (great for so many different applications), a couple individual single-use mini-saline bottles, face mask w/valve, penlight, scissors.
Off the top of my head that's about the absolute most I'd carry in a biking/commute-to-work first-aid kit.

Could get a little more advanced with a few more items that would make it a...
Better kit: All of the above plus: Sam splint, blood glucose monitor + test strips.

Then there's overkill:
Completely-over-the-top-and-ridiculously-unnecessary-for-commuting kit - All of the above plus some goodies from my personal home kit including hard collar, bag-valve mask, pulse-ox, OPAs...

And to all the kids out there, remember, do not attempt advanced procedures or use equipment that you haven't been trained for, certified/licensed for. You don't want to hurt someone and it can be a mighty a litigious world out there. Some countries more than others.