If it can help you, some days ago I went from 47th street to JFK by subway (A line) and connecting with the airtrain service at Howard Beach station. It took me about 90 minutes and two line transfers to get there with the luggage up and downstairs. In NY subway (subway in Calcutta must be more developped than that in NY)escalators or lifts are non existing. I arrived to JFK exhausted before taking a 7 hour flight but the best was the price, only 7 dollars (5 airtrain plus 2 subway)compared to the 45 dollar flat taxi fare.
About the bus, I have no idea but expect it to be more expensive and to stand heavy traffic jams in the way through Brooklyn and Queens.
If you travel with more people to share the cost, think about the taxi option, a few more dollars will be worth it.
If it can help you, some