Breaking the Barrier

Within the past year, my family moved to a new place.  We had lived in the place before for nearly my whole life, and I had some really, really good friends there.  I was all for this move, and I don't regret it in the least.  I love where I'm at, and I wouldn't change it for the world.  Being the 'new girl' at the age of 13 is super difficult.  The girls here already have their groups of friends, because they've grown up together. Plus, being homeschooled is kind of a disadvantage.  Don't get me wrong; I love homeschooling, and I definitely wouldn't change it.  It's just extra difficult, because I only see the girls at dance, and the 'socialization period' is very short; before and after dance for maybe 10 or 15 minutes at the most.  How do I become 'involved' with these girls' lives?  How do I make friends?  It is really difficult for me, because I am very shy.  I know that being shy can be taken the wrong way sometimes.  What if they think I'm stuck up?  What if they think that I think I'm better than them?  I don't want that at all.  I just want to be friends with them.  I'm really, really trying to create conversation, but what do I talk about?  What do we have in common besides dance and skiing?  I don't know.  I'd like to ski with them, but most of the girls don't ski where I do.  I try to smile, say 'hello' and 'goodbye', wave, make friendly gestures.  My mom keeps encouraging me to be friendly, and talk, but it's just so hard.  It's so hard to figure out how to break the barrier.  Sometimes a lot of times, it gets lonely.  I have my friends from where I used to live, and I keep in touch, but it's not like I can just hang out on the weekends.  This is one of the reasons that I love blogging so much.  You guys are my friends.  Even though I haven't met you in person, face-to-face, you are my friends.  I hope you feel the same way.  So, once again, the question comes back, lurking constantly in the back of my mind.  How do I break that barrier?  How do I ask if they want to hang out sometime? How do I ask that without it being totally awkward?  I. Don't. Know.  I need your help.  Have you ever been in a situation like this?  How did you get through it?  Can you give me some tips?