I think you might be confusing the Bethpage Bikeway Extension with the Nassau Greenbelt Trail, a mountain bike path that runs parallel to the Bethpage Bikeway much of its length, but then veers off into the woods at around Sunnyside Blvd and ultimately passes through the parking lot of Trailview State Park (next to Stop & Shop) before heading toward the technical mountain bike trail at Stillwell Woods. The Greenbelt also continues - as a hiking trail - to Cold Spring Harbor.

The Bethpage Bikeway goes from Merrick Rd on the south end to Bethpage State Park in the "middle," then continues as a bikeway to Woodbury Road in Woodbury. From there, a marked on-road bike lane leads you to the Syosset LIRR station.

I guess we can better answer this question if we know whether you are mountain biking or pleasure riding.