I'd not do a long term (overnight, over many nights) booking with a stranger either.
After all you're going to be in each others company a lot.
I will never be able to afford an overnight, so best of luck to you, and don't take the following comment as shade (it isn't).
Personally, I reckon you'd be pushing shit uphill to get a two night out of town outcall for 2k.
Overnight booking prices for like 12 hours are 2k at the low end and have seen them sit on average at 3k+.
Remember, for you this is a naughty couple of evenings with a lady you enjoy spending time with (and I can't blame you, I'd want to do that myself with my regular if I had the opportunity.), but for her it is a work trip where she has to be 'on' the whole time.
Also she might be potentially missing out on multiple bookings worth upwards of $350 a pop, doesn't take many of those over the course of four days (the day you're travelling to, the two days you're on site and a day travelling back/decompressing) to equal 2k for much lower investment of time and effort on her part.
I get it you're saying that during the day she can do whatever, but I don't think that'd make much of a difference in determining the price that you would likely be quoted.
Looking at one lady who is an indie worker and who sometimes posts here, her fee for 48 hours, which is kind of what you are really proposing is $12,000.
I'm not saying that the lady you have in mind would necessarily charge you 12k, but I think you'd be lucky if it was less than 6k.
The cost of the flights, accommodation and meals is probably irrelevant, as all those things are essentially for you not her, in that those things are just the cost you have to pay to have longer term access to her time.
Afterall she could just stay at home, only have to work like 6 hours over the course of 3 days, without having to be 'on' for nearly as long, and she'd still be $100 ahead on the 2k figure you are thinking of.
I'm happy to be wrong, and I hope it pans out well for you.
You might luck out and she is willing to potentially take a bit of a financial hit because she particularly likes you as a clients, or that she really wants to get out of town for a couple of days.
Those factors might work into the equation.
But the key word is 'might'.