It was made to be easy to do & with as little fuss as possible.
Just add a bgm page (usually, I disapprove of this sort of thing, but we agreed this would be for the best during the last site upgrade), add the usual info as if it were a regular song, then add a capitalized "BG" in the column where you'd usually add "LH" or "LI".
And that's it. The text will become purple & italicized, differentiating it from the played songs. I recall mentioning somewhere that it also subconsciously draws a visitor's attention to the playlist, making them a bit more prone to want to listen. Always a good thing.
Almost forgot. On bgm song pages you make, it'd be helpful to add a 'fact' to each one - "Used as bgm for Wackiness on the Rise." There's less confusion if visitors see something like that, but then read that the song was bgm for a show. No one will ask, "Why the hell does this have a page?"