Yeah, the subway system doesn't go out that far. You can take a bus to get to one of the subway lines, but your trip into the city will definitely go over an hour. The quickest way into and out of the city from bayside is the LIRR (probably only about 30 minutes), though it will cost a more than taking the subway or an express bus. Also, Bayside is a much nicer area than Jamaica, I wouldn't stay in a hotel in Jamacia.

Check out these sites: www.mta.info (this has the bus, subway and LIRR info and maps) and www.hopstop.com (you can put in the address of your hotel and where you want to go and it will give you the route by public transportation and how long it will take).