How to ask new advisor about her "style" in a professional way?
I still don't know what you have in mind as regards "style" but here are the things I think it would be useful to ask at the beginning:


How often she would like to meet and for how long.
Would she like you to get started with research right off the bat, or would she prefer that you start by concentrating on coursework and preparation for qualifying exams?
Are there any organizational, office assistant-type chores you can do to make yourself useful?  (Or if she has a lab, include lab chores in this question.)
A propos lab (if she has one), is there a lab manager?  What tips does she have to help you be an asset to the lab?
What are her pet peeves?  (I once asked this of my soon-to-be supervisor and she said, "humming and getting to work late" -- good to know!)
Are there any particular courses she would suggest you take in the first year?  (Familiarize yourself with the offerings and descriptions prior to the meeting.)
Communication preferences (email vs. phone vs. stopping by her office).  What you're trying to find out is 


what method works best when you need a quick answer
how she would prefer to get hold of you when she needs a quick answer
what phone hours she keeps, e.g. don't call after 9 pm, don't call before 10 on a Sunday, don't call during the dinner hour which is x - y pm or whatever they happen to be in her case
what turn-around time she expects from emails (e.g. 24 hours vs. there was a question here at Academia a little while back about a professor who would send an email and expect the student to pop up in his doorway within five minutes)
what she finds annoying (i.e. what to avoid)


(This would be a good time to let her know your communication preferences, for example, let her know about any chunks of time when you like to turn your phone off for your sanity.)
Any other tips?  (Here she might say something like, make sure to find one or two hobbies, try to attend all seminars and keep a seminar log....)


Note, I would not start out the meeting with a barrage of questions.  Many may be answered naturally during the flow of conversation.