There aren't that many flights from BOM to PNQ. In general, I'd recommend the car as well. Last time, I needed some 2.5 hours from BOM airport to Pune - western parts. When I take the extra time needed for check-in and security, the time going from your hotel in Mumbai to the airport, the time for going from Pune airport to your destination and compare that to the travel time for the car, then I'd still recommend taking the car. It is almost as quick as taking the plane, you have a much higher flexibility and you don't have any delayed flights.

A few colleagues flew this summer from BOM to PNQ. The plane had some 4 hours of delay and they needed another 2 hours from the airport to the office.

Are you going to stay in Pune or will you travel back to Mumbai the same day?