We were only dating for 4 months, she wanted the LTR upgrade but I said I couldn't due to circumstances in my life. I felt her interest going down because of this so I made the first move and broke up with her via text (beta/stupid?)

This was about a week ago. Should I wait another 2-3 weeks, then contact her? I want to start dating/having sex with her again. She lost interest first but I'm the one who technically broke up with her so I guess the ball is in my court. I feel like the only way is to tell her I'm willing to only see her. She had an issue with me seeing other women and it added to the reasons why she lost attraction. Obviously other girls finding me attractive turns her on but she want's/wanted to be the only girl for me. Hence her wanting an LTR. I feel like me breaking it off and then texting her to get together and see what happens makes me look needy and like I cant live without her.

What can I text her that won't sound needy or desperate? She's probably gonna want to talk about it too. Should I throw that in the text as well?