From the bridge you can go east on Queens Blvd.
make left onto Jewel Ave. you'll see on your right the intersection of Yellowstone, Jewel is on the otherside of the blvd when you cross it.
Take Jewel ave to Main st. and make a right
go to 73rd ave and make a left
go to Francis Lewis Blvd and make a right
take this all the way to Sunrise Hwy and make a left
you'll soon be riding along side the LIRR. you'll be able to see the Babylon train station from Sunrise.
For an early Sunday morning the traffic isn't so bad on the Sunrise, but this is a pretty direct route.
Good luck