A first aid kit that bikes with you must be light and compact. So it should cover only the basics -- stuff to get you back to the car without bleeding all over, and stuff that may keep you from aborting the ride.
I use one side-pocket of my CamelBak to hold first aid supplies. (The other side-pocket is for riding glasses.)
One bag contains major dressing supplies, one is for bandaids and prep pads, and a third is for medication.
For wound cleaning, I have two individually packaged benzalkonium chloride towelettes. (These also clean potential poison ivy oil.) I have two insect sting relief pads, which are also useful for stinging nettle. And I have a tiny packet of hydrocortisone, which I probably don't need.
In case diarrhea threatens, I have two Immodium (loperamide 2 mg) pills. Because I'm a doc, I pack a prescription Zofran 4 mg pill for nausea. Great if you have some in your medicine cabinet at home. Otherwise, you could use over-the-counter meclizine 25 mg (Bonine or Dramamine II) -- it works for mild nausea.
There are two 25 mg diphenhydramine (Benadryl) pills in case somebody has a bad reaction to a bee sting.
I bike all winter long. Not on roads. Up in the brush, snow and mud. And in the summer, I'm in Utah's high altitudes, where it can turn cold and nasty in a hurry. So I pack hypothermia gear. The goal is not just to stay warm on the trail; it's to stay alive if I'm lying on the trail with a broken leg.
So, in the bottom of my main CamelBak compartment, I always have a cheap throwaway rain poncho, a foil hypothermia blanket, and a Powerbar.