At some point soon, there will be an App whereby you can hum or sing portions of a nigun into your Iphone and it will identify the names of several songs that you might be looking for (if such an App doesn’t exist already).
I think they just called it Bagleiten on the album. That might not be what it is really called. It might not even have a name – like some very old minhaggim songs, such as the tunes used for davening on Yomin Noraim and for Chassunahs. Or they may have descriptive names like “The alter Rebbe’s nigun for negel vasser.”
I asked my son, who is an expert on old and classical Jewish Music, and he identified the tune as “Bemotzoei Yom Gila”. He did not yet tell me where and when it’s from, probably because he is at work and busy right now.
That album is the only source where that niggun is identified as Bagleiten. If you Google Bagleiten, a lot of different things come up. I think it means to say goodbye to someone.