PLUSBUS, according to the website:

is a cheap bus pass (like a travelcard) that you buy with your train ticket at any station ticket office, by ‘phone or online. It gives you bus (and tram) travel to and from the rail station and around the whole urban area of town that’s at the start &/or end of your train journey.

Not worth it it seems for students, who already get a concession and because season passes are not available in Edinburgh.

There is no equivalent at the East Lothian end, which is a limitation.

PlusBus Leaflet Quick Scan