There is a regular Volvo bus service from Kolkata Airport to Howrah. The buses start from 8 am until 7 pm, and a bus leaves every 30 minutes, and the journey should be from 1 hour to 1 and 30 minutes.
You will be able to get the Volvo bus from the right side of the main entrance of the Kolkata airport. I am assuming you would like to be dropped at Howrah station and the bus stops near platform numbers 8 and 9.