Many weekend LIRR trains enroute to Montauk use the main line, a line that runs through the heart of Nassau county and serves major hubs like Hicksville and Mineola. Many Montauk trains take this route via a Central branch connection between Bethpage (B tower) and Babylon. But most of those trains, do not make any stops along the main line, even skipping Hicksville and Mineola. That forces many people who wish to travel to Babylon and beyond, to backtrack west to Jamaica, then ride right past their station, losing an hour or more of their time and an extra $5 or so each way. The reason as to why this is done seems to be that the stuck up people who take the train out to the Hamptons cant be bothered with a few minutes of extra running time due to a stop. But in Hicksville the speed limit is around 20mph so a stop can be made without much delay.
For example, traveling from Westbury to Montauk, I have to get the 6:58am westbound train from Westbury (or the 7:28am from Carle Place) to Jamaica to get the 8:10am eastbound train going to Montauk.
In the evening if I want to take the 5:35pm westbound train from Montauk, I have to ride to Jamaica, get the 8:46pm train to Westbury. Had the train in the morning made a stop in Hicksville, I would've been able to get the 8:07am eastbound train from Westbury, and get the Montauk train at Hicksville at 8:30am or so. Going back, I would've been able to get off at Hicksville around 7:50pm and have gotten the train to Westbury which would've gotten into Westbury at 8:03pm.
There is absolutely NO REASON, no logical reason, for Montauk trains to skip Hicksville. By adding a Hicksville stop, it would save travelers in Nassau much time, as well as make the LIRR a more attractive option for folks in Nassau who wish to travel out east, instead of driving.
As far as using the Long Island Bus system to reach Babylon, it would take hours and isnt even possible on Sundays because most LI Bus routes dont start running until after 8am.