Bangkok is not a cruise port, but is served by the ports of Laem Chabang and Klong Toey. Combined, the port of Laem Chabang and Klong Toey is the port of embarkation for only one annual sailings from Norwegian to Asia.
Prices are about the same throughout the year. Overall Bangkok is rather expensive compared to other ports. Check out the chart below for the monthly average cost per day (Cruises only depart from Bangkok between January and March).