What items should be in a bare-minimum first-aid / emergency kit?
Water
Some sort of antiseptic, ideally something like a small bottle of Betadine, though regular ointment/cream will do fine, and it wouldn't hurt to have both
Gauze pads, in a couple of sizes
Adhesive tape
A few large Band-Aids
Some tissues or cotton pads for wiping off a wound


And, of course, cell phone, money, and ID (placed somewhere where people can find it).

I have my name, address, emergency contacts, etc on a gummed label stuck to the top bar of my bike and covered with clear tape