At that point, if she lists an email on a site she controls, I would tell her you reached out for a date request X amount of days ago and you are just following up by email since she may not have seen your text request for whatever reason.

You should definitely follow up. I’ve had clients text or email me before and their messages never actually came through. If they hadn’t followed up, we would have completely missed each other. Even if she’s on a FMTY, she should still have a minute to confirm she received your message and let you know she’ll reply when she’s able. If you don’t get that kind of acknowledgment, assume it got lost in cyberspace.

I would give it two days max. Then, I would follow-up and give it two more days. I have had plenty of situations where my initial message was missed or looked at and forgotten by accident. I think one follow-up is reasonable.

But I I will generally send a followup in case my text just got lost in the shuffle. It does happen, as as with emails. Four days seems like a long time to wait, but what was prior experience like when communicating, I would use prior experience as a guide there.  

 
In this case I might not even mention the earlier communication and just send a request for the appointment. If you still don't hear back in a day I'd move on.

Look, good providers are nearly one in a million - that means you are not the only one.  If you know they're worth it, book in advance.  If you haven't heard back in a couple of days, send another message - sometimes things get lost in the shuffle.  But great providers have excellent TCB, and if you haven't heard back a couple of days after the double tap, then you might start to consider if you fucked up somewhere.

And then move on. There are too many quality fish in the sea.

We respond usually within minutes at the very worst with hours.

Reputable agencies have a booker who responds to your requests in a timely manner. Independents, who work through a booker, are very good, too. Independents doing their own bookings are YMMV, depending on their attitude, character, motivation, and organization.

I've had a 70% success rate...the ones that responded promptly, like within a few hours, clearly value my business. My first two that I picked did not respond at all. Then the third one responded back in less than three minutes eager to set a date. Priorities.  

Is it possible you did not contact her with her preferred method? I sent a text to one provider and got no response, but when I used the form on her website, she emailed me within a few hours. Presumably she wanted all of her contacts to come through her website.