Me and my wife started journey on Aug,15th from Mumbai to Bagdogra (Siliguri) Airport. We didn't had any booking to travel from Bagdogra to Gangtok so we took local shared taxi (like Toofan) for which they charged 500/person (usual rate is 300-350, but since main highway was blocked due to land slide, we had to take another route which took 3 hours extra)
FYI: you can book "wizzride" shared Innova which will cost you around 760 per person but it's worth paying. You can book your seat online also.
After spending close to 6 hours finally we reached Gangtok and checked in to our hotel (summit Denzong) which is at walkable distance from MG Road.
Make sure you book your hotel near by to MG road or else you will end up spending more in local taxi and you might not get taxi during late night.
Later in the evening we booked a taxi for local sight seeing. Driver Uncle was really nice in nature and helped me to book Nathula pass Innova at a very cheaper rate. ( His name is Mr Rupendra, Contact: 9732792636)