I wouldn't text her about the climbing. I believe in the attitude - I don't have to explain myself to her about what I am doing, where I am going, and who I am with.
What is the purpose of sending her that message? So, she feels less awkward? Who give a $hit! You're assuming she's going to feel weird, but maybe she doesn't give a crap about it.
I see this with folks who are just figuring out DBing and getting a handle on themselves - wanting to reach out. You're probably not wanting to do this with the intention, but at some level you want to see what her reaction will be and if you can glean anything from her reaction about how she feels about you.
Just let it go! She gave up the right to know about whatever you're doing when she ended things.
Also, such a message comes across as needy. You're doing what you're doing and that's that. I am sure she assumes she'll probably run into you somewhere. Are you going to text her if she might be at a fav bar, restaurant, game whatever, so that it's not awkward for her? C'mon!
Go live your life and do what you need to do. I know I just smacked you upside the head, but you asked, and that's what these forums are for.
You're not doing yourself any favors by worrying about her and her reactions.
