Is it worth approaching this girl again who I barely know?

So a few years ago, I saw this girl in my school, we didn't know each other. On the last day while going home, I saw her, approached her and we had some small-talk. I sent her a friend-request on facebook.

Sadly she didn't accept it. I was becoming unsure, deleted it, then regretted it and sent it again. I didn't know that she would get new notifications, it happened a few times. I know it's bad and will never do it again. And she ended up rejecting it, understandably.

So the next few years we occasionally saw each other on the bus going to university, we're not in the same one. It's kinda weird because she avoids me a little (like making sure that I get on first) but then she sits where I can see her. Once she even checked her timetable and I could see ALL OF IT. Like if she thought I was a creep she'd make sure I never see it. Sometimes she sits in a way so that I can see her, but when she notices that I saw her, she avoids me, like walking really slowly and letting me pass?

Once, we went on the train, and I actually saw my friend. I told him the story of my failure, and he started looking at the girl, probably in an obvious way,, so that's another L for me. He started teasing me "what I'd do if he dated her", but also encouraged me to approach her again.

Another incident: I talked to a girl in Uni who I shared a high-school with, and I found out that she's friends with the original girl! So I told her the story of my tragic fumble. I friend-requested this girl (normally, this time) but she rejected lmao. After that she started smiling at me a lot, but I was oblivious and stopped having convos with her and now, she looks at me as if I were a bug... maybe the original girl having a friend who hates me doesn't help lmao.

So, is it worth approaching this girl again? Writing this down, I'm starting to realize that I was a dumbass lol. But I keep going forward and don't let my spirits be crushed.