While it is feasible to do it , it would probably take at least 2-3 busses to do so. CoachUSA/Shortline has a bus route between Exit 14 the Park and Ride in northern Nanuet to Tarrytown NY. Once over the bridge in Westchester, the BeeLine buses can get you from 1 town to another town. The bus to Tarrytown goes from Exit 14 to Exit 12 in Nyack before crossing the bridge. If you live in Piermont the Nyack stop may be closer to you.
The TappanZee Express lets you off at the corner of Route 9 and 119-where you can pick up the Bee Line Bus 1/1T south to Dobbs Ferry.
The Exit 14-Tarrytown ride is approximately 45 minutes, while the Tarrytown to Dobbs Ferry ride takes approximately 25 minutes. You still have to allow wait time and the time for the transfer, so this route is likely to take you 1 1/2 hours.
I hope this helps.
Licensed Real Estate Broker
Prudential Joyce Realty