Travel from New York Port authority to Brookhaven National lab via bus( or any cheap method)?

I have a chance to visit Brookhaven National lab for the remaining summer, but I am not very good with traveling. How would I get a bus to Brookhaven National lab from the New York Port Authority (8th Ave)? I am planning a round trip.
I depart 7/31/16 and will be in the New York port authority at 3:35pm or 9:30pm and have to return home at 8/19/16, being at the New York port authority at either 6:00am or 12:30pm respectively. I do not think the depart and leave dates can be changed, as my housing is fixed.
The least amount of exchanges via bus/train/whatever cheap would be preferred. Thanks.
Best Answer
I messaged my advisor and she informed me that I would need to take the train from Penn station to Ronkonkoma and then Taxi to BNL. Thanks for the help.
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