Never had anything like that, but I did have an arrangement where I met the girl at the same time and place every week for over a year.  I did not pay up front, however.

why not ask her  

Seeing as 2K is in the realm of what many ladies charge for an overnighter or 24 hour session type of thing, I wouldn't expect her to be yours for a full week.

Your probably more on target with your assessment of having to work around her schedule. Personally, I'd make sure you clarify everything before venturing into a situation like that.  For example, if you got a single one hour appt per day for 7 days your not getting much of a bargain for the 2K your paying upfront.

Depending on what you are looking for, some ladies will negotiate a reduced rate for x number of hours that you can use any way you'd like. One lady I've worked with in the past offered ten hours worth of time used as you see fit for $1500 paid upfront which was a 50% discount of her normal rate of $300/hr.