Where will you ride? In addition to being prepared for flats and emergencies, as others have given you ideas about, you need to consider how vulnerable you will be by yourself. I am a mountain biker and now a roadie, too, and there are some places in each category I will not ride alone. Think about what possible dangers you could encounter: from other people, animals, trail hazards/vehicle traffic, and then pick the safest places for your first solo adventures. Wherever you go, make sure you either know the area well or have a good map. This comes from my own experience of going exploring and ending up doing more miles than anticipated! A GPS is great for solo riders! I use mine quite a bit. It's fun to look at the maps of my trips when I get home. I printed up my favorite routes, so I can leave a map of where I'm going for my husband.
Another safety factor: not only does my husband know where I am and when I'm due back, we stay in contact during the ride. We have an informal schedule of when I'll check in, and he'll call me first if he thinks I should have called. We usually touch base at my half-way point and when I'm back at the truck, minimum; more contacts on a four hour ride.
For many of us, if we waited for company, we'd hardly ever ride. And you grow to love the solitude of the solo rides. It's a very freeing thing.