I think that in order to see her and to have your chance, you'll just have to be a bit gutsy.  I think that you should go over to her house, knock on the door (if someone else answers the door, introduce yourself as a neighbor, and ask if you can talk to their daughter), and ask to talk to her.  When you are alone with her, tell her that you know it's weird to be knocking on the door, but that you were hoping that the two of you could hang out over the summer.  Tell her that you had really wanted to ask her for her phone number, and that it never really happened.  You were a bit shy about it, so you were making up for that now.  I'm POSITIVE that she will think that this is so cute and she will be so happy that you decided to knock.  Ask her what she's up to for the summer, what she likes to do.  Don't just stand in the doorway.  Ask her if she will take a walk with you. See if maybe she wants to go to the pool with you.  Just be friendly and happy, and she will be too.  Good luck!