India should give Nepal transit to Bangladesh. It will help increase ties between India and Nepal. It will make help Nepal's trade with other countries. This should also be helpful to India's economy. Both nation's are friendly, and the deal will improve both economies through increased trade. It is also environmentally friendly.
While I am not familiar with any cultural nuances between those countries any form of connection, be it transit or trade routes from place-to-place, is positive for commerce and exchange of ideas/ customs. People have sought after trade routes since the dawn of civilization, because it was known that opening passages from one culture to another would lead to progress (economically, philosophically, or otherwise).
In my opinion India should give Nepal transit to Bangladesh. Neighbouring countries should help each other, and this would be a great way to help Nepal. They suffered so much through the earthquake and this transit would open so many possibilities for them. I'm not sure why giving them the transit would not be a good idea.
India will benefit by giving road access to Nepal to Bangladesh through India. The trade among the countries will increase as it results in more services across the countries. India should take the example of Europe continent and improve their trade routes to other countries. This in turn will help Nepal as well.