I went back the shopping place which is in front of the Customs office. As suggested by someone on internet, I purchased a local ‘Tashi cell’ SIM from a mall. Just for the sake of getting a Bhutanese cell number as a souvenir , I wanted to purchase the SIM. 
Documents required to purchase a local SIM
I instantly got the local sim and it activated within few seconds. I called my mother in India to check it.  Indian SIMs work upto a certain area of Phuentsholing. 
I went back to the transport office. Though I had to move from one office to other, it did not take much time and I got the permit. The employees were gentle and cooperative to me. 
After this, I was free to start my journey. Here, I would also like to inform that the first check point, where my entry permits were checked and I had to register myself and bike, was around 10 kms away on Thimphu highway. This is also known as Asian Highway 48 (AH 48). 
'My travelogue - in brief' 
  
I have posted some more information and relevant videos on touristhelpline.com
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