1.   yes it is rude to pester her with numerous calls the same day.  providers do have personal lives, and you have no idea as to what she might be doing. could be real-life stuff, or she has a lot of clients that day.  one call a few hours later should suffice, then you wait.

2.  no, it is not rude to call back the next day.

3.  no, it is not rude to tell her to only call you during certain times.  many providers will not call you back without some guidelines as to when it is safe for them to call you.

4. if you have waited a reasonable time, such as a day or two, it is probably time to move on.

Hope this helps,
Swim

If a provider does not pick up, is it rude to call back a few times throughout the same day?  If a provider does not return a voice mail, is it rude to call back the next day?  Is it rude to tell a provider to call only during certain hours, and to not leave any voicemails or send any texts?  Or should one just move on?

You might try using it the next time you contact an escort. My initial contact with almost all escorts is thru email. Some ladies only have email contact info.  I've heard plenty of stories from escorts about guys blowing up their cell phones. Once you've exchanged emails many escorts will then want to speak to you after you've confirmed a day and time.

Email is quite a bit easier to manager initially - they can be answered and returned 24/7 unlike phone calls. Phone is fine for talking and making arrangements or confirming appointments, etc. No one loves the cell phone blowing up all day and night

she probably won't even notice how often you've called. It shouldn't be rude to keep trying her every two hours or so until she picks up.

More and more, unless I know that she checks her email, I usually turn to texting after the first call fails.

If you are contacting a lady by phone and she does not answer calling back a few times same day is a bit much IMO.When you called the lady did you leave a message asking to be contacted back?Many gents contact us because they want to have a discreet time we do not know if it is okay to call you back.When I did have a number listed if a gent did not leave a message saying I could call him back whenever I got the message I did not return the call.The provider does not know your situation and maybe she was busy at the times when you called.I have many gents when setting up an appointment tell me not to call their phone they are in town or they give me a certain day and time to call.So,I do not think it is rude at all to let the lady know you do not want texts or voicemails.I also do not think it is rude to call the next day but one time and again that applies as I said above about leaving a message.
This is why I am Email Only because many of the times I was not available to answer the phone or people are around.If she has an email listed I would try that as a method of contact and see if you have better luck.

If that's rare, then you aren't the type of provider I'm doing a poor job of describing who can only be reached by happening to call at a time when she's answering her phone. With them, voicemail is not an option, obviously.

If the OP has an aversion to texting, he might give a second thought to overcoming it, especially for those reaching younger, crazy-thumbed types.

Dude, bro . . . I had a terrible time contacting providers by phone. In the beginning, I had a pristine new hobby phone, and the first 4 providers I called, it went nowhere, at first no return calls, then my location was too far, yadda yadda yadda.  I found that I had better luck when I contacted providers by email and tried to set up appts about one week in advance.