I have been texting this girl for the last few days and she has been showing lots of interest in me. Everytime I mention about meeting up,it is always a bad time. The thing is she has had some very valid excuses and her parents are worried about her meeting because they know that we just met and this girl was just recently killed in our area which kind of hit home for a lot of people in the area to watch out for what their kids are doing. I know she does want to hang out because even though she says that she is busy, she will start spitting out some of her own ideas of what we should do together. How do I make her and her parents feel more comfortable about me?

Good luck, parents involved in the situation makes it a bigger hill to climb

Set a boundary, she won't respect you if you continue to be soft on her. At the same time you don't want to be a dick, but rather firm and assertive.

"I think you and I would have a lot of fun together, its unforunate we cant make ends meet right now. Give me a shout when you're ready to chill"

give it some time. shes busy? get busy yourself and find some other chik. stop thinking how do i get her to date me.