score:3
Not sure if this is "public transit" by your definition, but the private Suburban Transit bus company, a division of Coach USA, operates a scheduled bus route between Monroe and the Port Authority Bus Terminal. You can easily get from Brooklyn to the PABT by subway.
You can use their search form from "New York, NY" to "Monroe Township, NJ", or here is a PDF timetable for Route 300. There are seven departures on Saturdays and four on Sundays. The Rossmoor North Gate stop appears to be very close to Exit 8A. Travel time from PABT is scheduled for just under one hour (subject to traffic, of course).
The regular fare is $18.25 each way.
Upvote:1
According to this unofficial New Jersey bus map, Middlesex County operates a local bus service, possibly called either MCAT or Community Shuttle. The M1 and M6 routes appear to serve Monroe Township, and connect to rail service at New Brunswick and Princeton Junction respectively.
Their website doesn't seem to be working for me right now, so I can't confirm this or find the official schedules, but it may be worth investigating as another option. Anyone who finds more details is welcome to edit them in.
Upvote:2
I don't know if this will be useful to anyone else, but I found a bus stop in East Brunswick 12 minutes away on RT 18. Only saves $2.10 for a senior citizen, but for other travellers it saves $3. Probably will use that if the usual traveller brings company.