S.W.
My daughter is just like that lol. She is 4. I was also the same way. The best advice I have for you is to slowly introduce her to a variety of situation with you there as backup. You have to push her comfort level just a little, but not too much only you will know what that limit is. Have her do small things like hand the money to the cashier at the store, stay at the gym daycare for a 1/2 an hour etc. It is a gradual process. Shy people usually grow up to be confident people, but also people who are very picky of who will be in their lives. I have only a few close friends & I consider that a good thing. Above all remember there is nothing wrong with being a shy (cautious) person & do not label her as shy.
Brekka
Btw my son is the complete opposite of my daughter & I get embarrassed by him frequently (example he wanted to kiss the cable man). So there are definitely pluses to having a shy child :)