Six miles isn't that far. You will always be at most 3 miles from home or work. Point is, that if you don't mind walking a couple miles, you can probably get away without flat repair gear. Maybe ride with a pump. Most flats leak slowly enough that you can ride 15 minutes or so before you lose pressure.

Fenders are nice when it rains or there is water on the ground, but not essential unless you don't want to get soaking feet and a streak up your back (some people don't care).

I've never found a bell or mirror to be esssential. This probably depends to some degree on your route.

Lights are a legal requirement in most places if you ride at night.

If you will be riding in snow or cold temperatures this is easily doable with the right gear (yes, even well below 0F), and potentially life threatening without. Studded tires are strongly recommended. See the winter forum section.

For me, a cell phone is essential, if for no other reason to let my wife know I'm not dead if I need to stop for a mechanical issue.

I never bothered with water on my commute (was 45 minutes, now its 4) or a cycle computer.

Paul