You can travel to Bhutan by all 3 means of transport viz. flight (Delhi, Gaya, Bagdogra, Kolkata, Mumbai and Guwahati to Paro) ; train (not recommended much as it is time taking) and road(you can travel to Jaigaon on Indian side) and from there cross to Phuentsholing). Once you reach there you can visit the following places - Thimpu, Paro, Punakha, Phuentsholing
Pls check this itineary :
Day 1: Arrive in Paro, travel to Thimphu
Day 2: Thimphu
Day 3: Punakha
Day 4: Punakha to Paro
Day 5: Paro
Day 6: Tiger’s Nest
Day 7: Fly home or continue to your next destination
Below was our itinerary: 1st Day:Pickup from IXB (Bagdogra) and Transfer to Phuentsholing (Immigration Formalities) Night Stay. 2nd Day:Phuentsholing to Thimphu, Evening Stroll Market and Night Stay.
3rd Day:Thimphu Full Day Sightseeing.
4th Day:Thimphu to Punakha, Sightseeing and Back to Thimphu and Night Stay
5th Day:Thimphu to Paro, Local Sightseeing and Night Stay
6th Day:Paro Full Day Sightseeing and Night Stay.
7th Day:Paro to Phuentsholing and Night Stay
8th Day:Drop to Airport (IXB)
After just entering from the border gateway of Bhutan, you'll get to see a big market. Don't miss that. It's very cheap according to the INR so just take everything that you will need to have with you during the trip like foods, drinks, snacks, medicines and other necessary stuffs.