This works fine for me with my set of 8 Bside songs. Do you have them labeled as BSideSong1, BSideSong2, BSideSong3, etc.?
If you don't hear anything when attempting to play them, then try the following: load in, press the walkman switch side keybind, press the walkman rewind button and let it rewind for a couple seconds (you should hear the mechanism rewinding), then play. You should be hearing the end of your last Bside song. After that, you should be able to rewind to the beginning and start from your first song. When trying to add my own Bside songs I was confused for a while, before realizing that it starts at the end of the last Bside song when you first switch sides (since that's actually modeled). Hope that makes sense. I would upload my song set if it weren't copyrighted music :(