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].
Until further notice there is a temporary timetable in operation.
Monday to Saturdays for most of the day there are two buses to Douglas. One turns right and goes via Shore Rd, Gansey. The other goes via Port Erin and Colby. Both routes join just before Castletown. Early morning most buses go via Port Erin. 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.

Also the number 28 runs to the Sound and Port Erin. This runs on Saturdays and Sundays (not running in 2022).
The N8 runs on certain evenings between Port Erin/Port St Mary and Peel (not running in 2022).

All buses are run by Bus Vannin
 
Check the Bus Vannin facebook page for last minute changes to schedules.

When the Billown Circuit (Southern 100) is in use, buses will only run between Douglas, the Airport and Victoria Rd in Castletown (passing the Steam Railway Station). There will be some buses operating between Douglas and Port St Mary via Foxdale (not serving the Airport, Castletown or Ballasalla). The Steam Railway will operate as normal.

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.
More information here.

The Manx Electric Railway (MER) starts at Derby Castle at the north end of Douglas Promenade.  The MER travles through the lovely Manx countryside to Laxey and Ramsey.  At Laxey the Snaefell Mountain Railway runs to the summit of Snaefell.
Most of the Douglas buses from Port St Mary travel along Douglas Promenade to Derby Castle.  Alternatively take the Steam train to Douglas, walk along to the Promenade and catch a bus to Derby Castle.
More information here.