How to get to know girl with strict parents in highschool?

I(M15) have recently have started trying to get slowly get to know this girl in my class(F15) who I will refer to as Vanessa. I’ve barely talked to her so far but managed to get her number around the holidays. I messed up and think I was being a little too pushy by trying to plan dates on two occasions to the movies, however, I acted polite about it and didn’t bring it up when she said she was busy. Following new years, I attempted to get back to planning but she apologized to me and said that her mom wouldn’t let her go. Some of my friends say that she wasn’t interested from the beginning but I feel like from the few interactions her and I had that she is being truthful. I want to know how I can make it clear that I want to get to know her and express my feelings without coming off as desperate. For reference: I did not talk to her for a brief period of time when she said she couldn’t originally and I’ve made the mistake of being a little distant and not talking to her much recently out of fear that she doesn’t like me. I feel like my insecurities and obsessive planning might push her away.

TLDR: I like this girl and have been unsuccessful in planning dates because of her unavailability/“strict” parents. I wish to know how to advance things from here on out.