I'm with everyone else in the 'likes to ride alone' category.

I didn't start feeling that way overnight, it took some time (weeks, months? - that, I don't really recall) to get up the confidence to head out alone.

Like everyone else said, carry equipment to change a flat and know how to use it, carry a cell phone and ID (I wear a RoadID bracelet, and I carry ID, contact info and a copy of my insurance card in a small thin wallet in my back jersey pocket), and a bit of cash in case you need it.

Don't force it, give yourself time. Start out riding alone on familiar local routes. Sooner or later it'll become not a big deal, and you'll ultimately either enjoy it or not.

Self-sufficency is always a good thing, though.