as to how to go about contacting her, including screening information?
If so, and you did not follow it, that could be the reason you haven't heard backA couple days ago, I contacted a provider in my area who requested that those who were interested in her services text her on one number, and if she didn't respond to text her on a second number that she provided.
At about 9:30 on Tuesday, I texted her, giving my first name but not my last and asking "if I could make an appointment at 4:00 tomorrow". She didn't respond, so I texted her on her second number 12 hours later, again, giving my first name but not my last and asking if "I could make an appointment at 4:00 today".
I haven't ever done this before so I'm wondering if I made a newbie mistake or if its unrealistic to expect a provider to respond that quickly. Furthermore, what do you recommend I do now?
....I always respond within 12-24 hours at the latest!!
In my estimation, what you described is a sign of a provider who does not appreciate their potential client's inquiries. Plus, the time the client spends researching who may be the best match for him. Personally, I have an understanding of the choosing process after having talked to people on how it works.
With that said, ask yourself who else you'd like to see. #2 on the list may very well be your ATF!!
If the original lady is behaving this way now, its not easy to predict a positive experience that you'll remember as one you'd like to repeat.
My 2 cents 
I highly recommend making sure that the lady you choose is newbie friendly. 
Thank you Krista, for your reply, I will definitely inquire into other providers in my area.
If you're not using a screening service, that's definitely a newbie mistake. Even when a provider lists her phone number, I always made first contact via my screening service.
When I texted her later, I always started with: "I messaged you earlier via P411..." That gives you some credibility, as opposed to an anonymous john who is just cold-texting her. Always use a screening service, & only see girls who are listed on your screening service.
Since this provider has two phone numbers in play, be aware of a possible bait & switch. --z
as to how to go about contacting her, including screening information?
If so, and you did not follow it, that could be the reason you haven't heard back
it doesn't look like you didn't do anything wrong. Seems like you followed her instructions all right. The posters above have offered some possible reasons, as to why she didn't respond. She also might have gotten a better offer than yours, like a multi-hour date that infringed on the time you asked for, hence you lost out. If she didn't reply to either of your texts, I'd say it's time to move on, there are plenty of others out there.
LLAP,
Swim
So I don't have a screening service yet, so that could be one reason. She doesn't have a personal website, just an ad. I did read the ad completely and she said to text her but one of the reviewers mentioned that he had called her so I don't know if that's a set in the stone instruction.
it is just bad manners and poor service not to reply to a politely written message. Even if I am busy at the requested time, or need more information, to complete the appointment/screening, I at least send a quick message back. What does that take, 30 seconds to say, "sorry I am busy at that time". I don't think that you did anything wrong per se, she doesn't have great customer service, IMHO. As someone else said...move on to door number two. Good luck!
although short notice may be a problem for some. But state a visit, day & time, how long. Express willingness to provide any other info she requires. Your phone number
At about 9:30 on Tuesday, I texted her, giving my first name but not my last and asking "if I could make an appointment at 4:00 tomorrow". She didn't respond, so I texted her on her second number 12 hours later, again, giving my first name but not my last and asking if "I could make an appointment at 4:00 today".
I haven't ever done this before so I'm wondering if I made a newbie mistake or if its unrealistic to expect a provider to respond that quickly. Furthermore, what do you recommend I do now?
We might be able to give you more thoughts.