Paro hosts the only international airport of Bhutan, from where one can hire a taxi to reach Samdrup Jongkhar, which is about an 11-hour journey. Bus services are available from Mongar, Trashigang and Phuentsholing, which can be reached by bus from the capital city, Thimphu.
Guwahati, India, is the nearest airport from where it's around three-hours long drive to Samdrup Jongkhar. If you're landing in Paro Airport in Bhutan, then from there it's an 11-hour long drive to Samdrup Jongkhar.
From Guwahati, India, a cab can be hired at the airport which will drop you till the border. It is advisable if you pre-book a taxi instead of doing it at the airport because at times, you may not get a cab at reasonable rates. If you're driving by yourself, then make sure to take the shorter route via NH27 and NH127D. If you're heading to Samdrup from Trashigang, then it's almost one day-long journey via Bumthang - Ura Hwy.
Travellers from Thimphu, the capital of Bhutan, will have to embark on a three day bus journey, switching buses at either Trashigang or Mongar before arriving at Samdrup Jongkhar. Direct buses are also available from Guwahati which will drop you at the border.
Since the town is small and the weather is also pleasant, one can easily get around on foot.