The flight from Kolkata (in India) to Paro (in Bhutan) is an international flight, as it travels from one country to another country. That an Indian citizen can travel to Bhutan without a visa does not make the flight non-international.
If international passengers are refused entry at their destination, the airline is required to return the refused-entry passenger to the passenger's point of departure at the airline's expense (although the airline will probably try to collect the cost from the refused passenger). To avoid this, airlines rigorously check the travel documents of passengers very carefully before allowing them to board. You will pass through Indian exit immigration and the airline's check in CCU. As an Indian citizen, you will be required to show an Indian passport with six months' remaining validity from your date of arrival in Bhutan.
It's possible that the Bengaluru > Kolkata flight will be delayed. Some flights are rarely delayed, some more so. You can get some (admittedly vague) idea of the flight's delay history on https://flightaware.com.
This is an important issue. Because you've booked two separate journeys (BLR > CCU, and then CCU > PBH), if the first flight is delayed or cancelled and you miss the second flight, the first airline will have no legal responsibility to transport you to PBH, and the second airline (if a different carrier) will have no obligation to reschedule you, and will also cancel your PBH > CCU return. Instead, you'll have to purchase a new CCU > PBH > CCU roundtrip.
Thus, make sure you have enough time to transfer. That means retrieve your hold luggage from the carousel, get the hold luggage to the CCU > PBH airline checkin counter before the check-in deadline, then line up and endure security and India exit immigration checks, and get to the departure gate.
The time you have to do these tasks will reduce if the first flight is late. For a really-don't-want-to-miss second flight, a conservative approach might be to schedule an overnight in CCU between the flights.