I disagree with your premise that pricing and specific acts are not to be discussed, but that could be if you are confusing a professional dominatrix with a prostitute. Many, but not all, pro Dommes do not engage in sex acts, so there's not quite the same level of concern about law enforcement entrapment that other sex workers might encounter.
That said, I'd recommend that you use the word "tribute" (see link for further details) instead of "fee" or "rate".
Unlike an escort, you should probably have A LOT of discussion about what you are - and aren't - going to do before you play. Believe it or not, most pro Dommes will have MORE respect for you asking questions. Just be aware that Their radar is going to be on "high", and if it comes off like you are trying to use Her as a 1-900 sex line for a jerkoff fantasy, She'll likely hang up.
I'm surprised to read that the tribute is not indicated on Her website. That's kind of unusual. The going rate for a pro Domme can be $200 to $500 per hour, depending on how specialized your interests are, plus tipping is appreciated. I know that seems like a lot of money, but take into account all of the equipment costs and training on their end. Your life might literally be in Her hands, depending on the activity, so ask yourself -- is this the best place to try to cut costs? Same deal as an escort . . . just put the money in an envelope and set it down, and don't make a big deal about handing it directly to Her.
This "active and successful mistress" most likely has an email, so just send Her a very polite note -- you don't necessarily have to be submissive, yet, but you can be -- along these lines (note the use of Title Case for Her and lowercase for you):
"Dear Mistress _____:
my name is _____ and i would respectfully like to ask if you are seeing new clients. i have reviewed Your website and believe that W/we might have compatible interests. my interests are {list of BDSM activities}. Since it was not mentioned on Your website, might I also inquire about Your tribute, understanding that Your tribute might vary depending on the type of play involved?
i hope to hear from You at Your earliest convenience. i may be reached at {contact info}.
Thank You for Your kind time and attention.
Respectfully,
{your name}