The Suffolk Transit bus passes through but not a 'greyhound.' The Greyhound stations are in Hempstead and Brooklyn with bus stops in Nassau. Closest to the airport is the GH bus stop on 700 Motor Parkway in Hauppauge. The next Greyhound bus stop is in Babylon at 238 Deer Park Road.
There is a Hampton jiney bus near the airport but does not serve PABT. You would have to take the S57 bus to either Ronkonkoma or Sayville. From Sayville Station take the train to Babylon and take the Babylon train to Jamaica and connect to the E subway
The Ronkonkoma train station is on the other side of the airport about a 5 minute cab ride, that will take you to Penn Station (34th street). The Hampton Jitney bus has a stop at MacArthur airport, you will have to check their schedule and make a reservation on their website but it should take you to Midtown.
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