Where did I go wrong?

There was this girl that I liked and I sat next to her in class, but I was so shy that I couldn't even talk to her. I wanted to, but I just didn't have anything else to say. Well, I'm not he best at starting conversations. I've only talked to her a few times before class. So one day I brought up the courage to ask her out for lunch and she said yes, she'll give me an answer the next day. And the next day, she said she couldn't make it cause she had to go on some trip. Okay. So I ask her again 2 weeks and the same thing happened. She said yes again but the next day she told me it isn't gonna work out. Me being confused and naive didn't really know why she would tell me yes then no. I felt kinda bad that I put her on the spot by just asking her out without really talking to her so I went to this bakery and got this really nice cake for her, like a gift to apologize. Then when I gave it to her she got really embarrassed then I knew she didn't like me. I felt really bad because it was unfair that I put her on the spot in front of her friends, but I didn't know that she'd react in that way. Now we don't even talk to each other, but I hope if I see her again I can at least say something. Where did I go wrong with her?