Interesting question that comes up from time to time. I'm not sure there is any one answer as there are so many variables.

Hard to find any rates quoted online other than going somewhere like Warsaw Prison and doing the Domme addon to the basic incarceration fees.

In that instance it looks like 48 hours with Dominatrix M coming in and playing with you during the days would run around 3,000-3,500 USD in total depending on any extras you booked. Seems very cheap to me.

https://warsawprison.com/en/prison_stay_fees
https://www.dominatrixm.com/en/fees

I'd have to guess US rates would run more like 5K and up but I know that would vary depending on the Domme, the type of session and other variables. IE: how much interaction with the Domme vs extended isolation bondage or time left in cell/cage? Does she have her own appropriate playspace or would she need to hire? Are you looking for 24/7 captivity or or downtime outside of the fantasy?

I suspect Dommes who offer this probably get 10 or 20 inquiries for every session that actually happens.

Something like this has always fascinated me but the best I've ever managed has been an evening of play and an overnight under her control. Still, I haven't given up dreaming!

Would love to have some Domme's chime in with real data for the US.