From experience there is no danger for a female to travel alone if you travel wisely (be informed and stay away from potential troubles).
First time I left alone, I think I stayed 4-6 days just hanging out in my hostel room (besides going to buy some food next door) because I was too self-conscious to deal with people. BUT after 2 months travelling, I was like a happy fish in the sea.
I heard some weird stories about couchsurfing too, from girls sleeping at guy's places mostly, but I think there is a reputation system on the website, so I guess if you choose families or females with good reputations that should be safe enough. I never used that and never will though, it involves way too much socializing for me. I also avoid youth hostels, since they're jam packed with cool social people who really wants to keep being cool and social. Though it's perfect if you want to meet cool and social people. haha
Overall it's a really good way to overcome social phobia (for me at least), so I think you should really do it
Edit - I'm talking to you as if you were a girl, but in fact I have no idea. I haven't heard any story from guys about weird experiences with couchsurfing.