Questions: Relationships

I guess this is a follow up to my last question. I was hanging out with my ex girlfriend today at work (we work together) and she was chill the whole time still. Since I dumped her she'd always occasionally try and talk to me or say something to me. I initially ignored her because of her shitty friends mostly, and because I wasn't sure if I wanted her back, but I now I do. She's apologized like 3 times now, and she said she understands what I meant when I said I was legit busy and not cheating like she thought 😑. The only issue I have now is figuring out how I should go about the whole thing.
Like should I text her first? I told her she could text me if she wanted to after the whole valentines day thing, but she never did (I think because of her friends) but if she wasn't at least a little interested she wouldn't be talking to me and inviting me places. It would be out of character for me to text first, and I don't know what to say

I've just seen this post, and got me curious to ask it, what are your thoughts?

Are there certain actions/choices in life that you can't come back from; Like once you cross that line, you have to stay on that side. We have this mindset in other situations, perfect example is murder. Once you murder somebody, you ARE a murderer, and no amount of time after that changes it. Can people change or are they bound to the lines they've crossed in the past.