You can take a direct bus from the Mumbai airport to Pune

You can now travel from the Mumbai Airport to Pune without any hassle, as AC Shivneri buses have started plying between the two cities from December 16. According to a senior official of the Maharashtra State Road Transport Corporation, the buses will also be available from Mumbai airport to Ratnagiri district’s Dapoli.
The bus will operate from Mumbai’s Chhatrapati Shivaji International Airport’s Terminal 1, and the first bus will depart from the airport at 5:30 AM. Then onwards, there will be 17 trips to Pune throughout the day with buses leaving every hour. On the other hand, the first bus to Dapoli will leave the airport at 7:30 AM.

Reports also suggest that the bus service will be under the watch of two inspectors, who will be deployed to provide assistance and information to passengers.
Timings

The timings for bus departure from Mumbai are as follows - 5:30 AM; 6:30 AM; 7:30 AM; 8:30 AM; 9:45 AM; 10:45 AM; 11:45 AM; 12:45 PM; 1:45 PM; 2:45 PM; 3:45 PM; 4:45 PM; 5:45 PM; 6:45 PM; 7:45 PM, 8:45 PM; and 9:45 PM.

Shivshahi buses that will leave for Dapoli will depart from Mumbai as follows - 7:30 Am; 9:45 PM; and 11:30 PM.

There are a total of 24 AC Shivneri Volvo buses, and 50 Shivshahi buses.