Want to know wabout the shortest land-route between Nepal and Bhutan

The best way to go to Nepal from Bhutan is to catch a bus from Kathmandu to the eastern border . It may take about 18 hours to go to Bagdogra / Siliguri, From there buses are available to Hasimara or Jaigaon.
Indian citizens can travel independently in Bhutan. A permit is required .All permits are free. The total journey may take about one and half day to two days.

There are some combinations of road and train travel which can be combined to optimise the route between Nepal and Bhutan. Generally people avoid combining as it adds to inconvenience of changing mode of travel. So it is preferred to go by road using bus/ taxi / shared vehicle.

There is a town known as Kakarbhitta in Nepal-India border. You can reach it from Kathmandu or any other major place by bus or taxi and it takes about 10-14 hours. Once you reach there take a rickshaw and you have to cross the Mechi river bridge and reach to Indian side location known as Panitanki. From this Indian side, you can get a bus or taxi for Siliguri (West Bengal).

From Siliguri one has to take bus or taxi for Thimpu (Bhutan) and there are two alternate routes one is using NH17 while other is using Phuntsholing - Thimphu highway. Both the routes take about 8 hours to reach Thimpu. Sometimes direct bus might not be available and one has to perform the journey in parts.

Drangme Chhu is the biggest river system originating from Himalayas and consisting of its 4 major tributaries in Bhutan and it is 272 km long and then enters India where its name becomes Manas River and then it flows through the state of Assam.

You can combine rail and road mode to reach Nepal to Bhutan. This is because Bhutan doesn't have any railway line till now. Please find below the process by steps.
1. The train starting in Nepal from Birgunj station, you need to take a bus from Kathmandu to Birgunj which will cost you around 6 US Dollars.
2. From Birgunj to you need to come to Raxaul Junction, which is in India. So you need to take Indian Visa from Kathmandu. The distance from Birgunj to Raxaul is approximately 5 Km. So you can even take a taxi or have a walk.
3. From Raxaul to Barauni, you can have a train journey. If you start a train at 12.55 pm then you will reach Barauni at 17.45.
4)From Barauni, you need to change the train to reach Hasimara station in West Bengal. You will get many trains with duration change from 5 hours to 7 hours.
5) From Hasimara to reach Phuentsoling, which is a border city of Bhutan you need to take a bus which is cost-effective. Bus journey will take only 30 minutes to reach the check point.