How do I approach this?

Protect your heart?
You haven’t even met yet…

There are a LOT of flakey guys on line.

It sounds like he is either flaky, busy, not interested, timid himself, or some combination of these. In addition, the fact that you have never initiated a text exchange (you only reply to his texts) may be giving him the impression that you are not interested, but are simply being polite enough to respond to his texts (and too timid to formally turn him down). Of course this is without knowing the details of your text exchanges. If he already told you he is interested in meeting up with you, assume it is true and make it happen without tip-toeing around (if that is your goal as well). Though at this point, recognize he may have moved on. Still don’t assume. Be assertive and formally ask him to a date (formal plans) and be just as glad in the event he says no (that way you’re not stressed about not knowing his status and waiting around. After all, if you haven’t even met up with him yet, sounds like you’re not really emotionally invested yet anyway. Likewise, you should not hesitate to move on if/when that is something you want to do. There are plenty of other fish in the online sea (sounds like you have no problem getting asked out). If things don’t progress with him for whatever reason, I’m sure you’ll look back at him as “old hat” by the time you’re getting dressed for first date with the next one that comes along. Best of luck!

You are overly invested in someone you have not met if you feel at all aggravated.

He is not invested in you because a man who has never met you is not invested, nor should he be.

When a man keeps texting me, if he says I want to ask you out, I always say – I would love to, but if does not ask me out, I either stop responding, or I say “I appreciate that you keep texting, but it seems like your bandwidth is challenging right now. Feel free to reach out when you have more time”.

Instead of focusing on what they are doing before they matter as they are not your boyfriend, just observe.

Do not ask a man out on a first date. Ever. That’s his job, don’t take it away. Men who are unavailable or uninterested in you will go just for fun rather than turn you down, so it says nothing about their real interest in you if they said yes.

I’ve dated high powered, busy professional men and they WILL make time if it’s important enough to them. I’ve sent messages similar to what TallSpicy suggested because things seem stalled in messaging and it does work in the right circumstance. If he’s busy on a particular case, he should come back and say, I’ve got an end date of X on something I’m working on now and I”ll have more time after that, would you like to get together then. (And you say sure, hit me up around that time and watch what he does.) Or he will sit up and realize you’re walking away and just ask you out for a specific day.

Send that message and let this one go unless he steps up.