Cheapest way to visit Bhutan is to reach Hasimara station(West bengal) by train, then take a cab or bus to the bhutan Border situated in Jaigaon. You can cross the border by just walking. From here, you need to get an entry permit from the immigration office at the border, you'll either need your voter Id or passport. You can visit Thimpu and Paro cities in bhutan, although immigration office is at phuentsholling, so you can explore there as well.