How does one recover with any person you said something offensively cringey to? You think an sp is different somehow? Apologize. Be sincere. Be humble. But realize that your "recovery" will come in the form of not making the same mistake with the next person.
If you came across as a time waster, why not show her in the most tangible way that you value her time and send some $ or a gift card? I imagine her website has some suggestions for how to spoil her. Doesn't have to be much, even $20, and then send a separate message/email (don't fill out the notes field on an etransfer or gift card transaction) telling her that you're genuinely interested in meeting, you're sorry for coming across as a time waster, and if she's willing to give you a second chance you'll be happy to book.
In this case he should send the fee first and arrange a time after.
Fucking around with endless “I’m genuinely interested” texts is only going to aggravate the situation.