Advice on how to Repair a Relationship after a Misunderstanding

I’m writing because I recently had a misunderstanding with a friend in college and I’m not sure how to fix it. A few weeks ago, I went to lunch with a girl in my same program and we had a great time. We continued texting after that, but I noticed that things started to feel off.

Eventually, I found out that the girl’s roommate had invited me to a Discord server where she had been sharing information about me in which they had been berating me and calling me names. When I asked the roommate if anyone had wronged my friend, she said that someone (me) had made her roommate feel uncomfortable so she claims by saying that I knew she was intimidated by me when we first met. I explained that I didn’t mean it in a negative way and that I just wanted to clear up any misconceptions, but things continued to escalate and “bullying” ensued. The girl eventually started calling me a “weirdo” and a “creep” and threatened to kick me out of the Discord server. Since this situation I have not spoken in the server

The problem is, the girl I’m speaking with doesn’t have Discord or social media, so she’s receiving all of this information from her roommate. When I saw the girl in person, she seemed distant and awkward, and I noticed that she was texting her roommate and laughing most likely at me. I’m not sure how to move forward or if I should just try to forget about the whole thing and move on.

I’m not sure if I was in the wrong for what I said, but I’m willing to apologize if I did something to offend her or her roommate. The problem is, I’m not sure how to approach the situation or if it’s even worth salvaging the friendship. I would ideally like to continue our friendship and studying but am not sure.

There is also the issue that whenever we hangout or eat it is always me inviting her never the other way around , is this something I should keep doing? I don’t want her to feel as though she’s obligated to say yes.

Any advice or suggestions would be greatly appreciated.