I searched for this topic and couldn't find anything, so I posted my own but I've had the same question.
Initially, I created a spreadsheet calendar and sent to her at the beginning of each month. When I'm fully booked, that seems to work. I'm able to include the dates, number of guests, and any notes I wanted (like early check-in, etc). However, lately, I've had some last-minute bookings due to open dates and a few cancellations. I have two apartments and I'm about to add two more to my listing, so this is going to be more difficult and the cleaning lady is not too tech savvy.
Other than a spreadsheet, I'm not sure. Using a sync'd calendar sounds good but I'm not sure if she can handle that. I hope Airbnb creates a solution.