Hi Antara! From Bagdogra, the taxi fare to Bhutan is around Rs. 2,500-3,000.
Here is one taxi services you can look into: ne.cab/bhutan-car-rental. For other cab services, you can contact some of the travel agencies in the area:
1. Manorama Travels
2. Suvidhaa Travels
3. 99Taxi
4. Himalayan Vintage Holidays
Happy Travelling!