I used to be scared to death over the prospect of going anywhere by myself but then I moved across the country and was pretty much forced to be alone!! There was an arcade at the mall about 3 miles away from the dorms, and I would walk there alone almost every day for about 3 months. People would stare at me though, because I was rather different from everyone else.
The experence really taught me to be less self concious, and a lot more outgoing. Now, instead of hiding, I'll actually go up to people I've never met before and just start to chat.