I'm a nanny and have been for 20 years, I have had all sorts of handovers, from meeting at the interview and then being left after 15 mins my first morning to being with the mum for 2 months (4 month old twins), to be honest, as long as I know how long the hand over will be, I am happy with any, as long as they leave me a phone number I can contact them on if they leave me from the outset.
As far as I am concerned, I am a complete stranger and they are leaving a precious life with me, if they want to spend a week or 2 months getting to know me, then who am I to argue.
I agree with spending one or two complete days with the new nanny, then like others have said, take an hour off to go to the hairdressers or shopping, but at the end of the day, you have the final say, and if you feel comfortable leaving them all day, go for it, if not, hang around until you do. But give yourself plenty of time, don't say 2 days because others have said that, I would say give yourself at least a week, two if you can afford it, who knows how you will feel about leaving your baby.
I know I would rather that the mother went off to work completely happy with my abilities to care for her child/ren bacause she has seen them for herself, rather than for her to be worrying all day.
And to be honest 1 or 2 weeks with the mother is not a life time and will go pretty quickly.
Just go with what you are comfortable with!