Have you seen her before? If not she may not be willing to talk price in an email as it could be incriminating.  

I'm always hesitant to "name a price". I would much rather have the lady tell me.  How many hours are you talking about and how much of it involves sex time?  You may want to check out some other ladies in your area and see if any of them list full-day or overnight rates.

She opened the door about pricing, if her web site does not give you the needed information, then now is the time to discuss it. Most active and well reviewed ladies, if not otherwise specified, will expect their hourly rate times the hours together, with possibly a small discount for multiple hours. Tell her what you are thinking, because all she can say is no, but maybe you will get lucky and she is just dying to spend a fun filled day at an amusement park.

What is it worth to you?  Just to throw (meaningless) numbers out there, let's suppose that your answer is $500, and her hourly rate is $300.  She may be less likely to take an all day outing with you for that little.  However, I'd rather be happy with my purchase.  If I'd be willing to spend any amount to spend the day with her, it's easy enough to multiply her closest posted rate by what it takes to get you to the desired number of hours.

In short, are you worried about offending her, or worried about paying too much?  The answer to that question will be your guide.

I would never suggest a price.

I would ask once what she would want for her time.  If she waffles or throws it back to me, that would be the end of it as far as I'm concerned.