Advice from the old lady:
I'm born in 1969 ok. So of your generation. Here are a few things to keep in mind:
1. Do not beat yourself up over this. Most women are conflict averse and will NOT be direct. I'm polite yet direct, but I am the exception. Very few women will be straight with you. In my experience the ones who will be very direct will do so out of great abundance. When you have lots of good choices you have to make sure nobody is wasting your time. In actuality that saves you time too. This is a net positive. Value your time.
2. Quit caring about her (schedule/work/family/obligations) more than your own. Do NOT tell her what days you are free & submit those days for her approval....ask her to join you doing something you enjoy & were going to do with or without her. She's a grown up, she can say Yes or No. If she waffles? Tell her you can make other plans. Respect your own time. Put yourself first. If you won't or don't nobody else will, trust me.
3, Yes you should initiate and do the inviting. You are the man in the interaction. Give her some masculine energy to be receptive to. Do you want her wearing the pants and being the male in the relationship? No? Good. Be the man and make a move. That's the law of the jungle Tarzan if you want Jane. As things progress she can do for you & show investment, but especially early on you gotta be the man, man.
4. Less is more. Few words, make plans, chat in person, have fun. Text banter is great but its an advanced level skillset. You aren't great at it or you'd know you're a bad ass already; you'd be confident in that ability. So use text or the phone to make plans and then chit chat in person.
I know this is a bit rapid fire. If you do those things above it will help your interpersonal posture, which will benefit you, trust me.
Welcome.