There is a bus stop with a shelter at the end of the Promenade, on the side of the Primary School ( Scoill Phurt le Moirrey). Buses run to Castletown, the Airport and Ballsalla and Douglas via Port Erin or Shore Rd [most buses continue along the Prom in Douglas to the Electric Railway and Onchan].
Monday to Saturdays for most of the day there are two buses an hour to Douglas. One turns right and goes via Shore Rd, Gansey (this is the faster of the two). The other goes via Port Erin and Colby. Both routes join just before Castletown.  Sundays are similar to the Monday to Saturdays timetable but with slightly less buses in the early morning.
A summary of buses between Port St Mary and Douglas is below.

The Steam Railway Station is a 10 minute walk from Mallmore in the Port Erin direction.  Trains run most days between March and October.  Generally there 4 journeys each way and on occasions 6.  During TT race week a commuter service with restaurant car runs.
Steam Railway Timetable
More information here.

The Manx Electric Railway (MER) starts at Derby Castle at the north end of Douglas Promenade.  The MER travels through the lovely Manx countryside to Laxey and Ramsey.  At Laxey the Snaefell Mountain Railway (SMR) runs to the summit of Snaefell.
The Douglas Bay Horse Tramway runs between the Villa Marina and Derby Castle
Most of the Douglas buses from Port St Mary travel along Douglas Promenade to Derby Castle or the Villa Marina for the Horse Tram.  Alternatively take the Steam train to Douglas, walk along to the Promenade and catch a bus to Derby Castle or the Villa Marina.
Timetables
Manx Electric Railway (MER)  Snaefell Mountain Railway (SMR)
Douglas Bay Horse Tramway (DBHT)
Further Information
MER SMR DBHT