Unless you know the language this probably won't do you any good, but if you put "traditional Bangla music" in the search at youtube, things like this come up. Here's Another Sample.

Not sure if she ever sings in English, but the write up with this one sounds fascinating:

Certain specific tendencies can be observed in the works of Tagore as a composer in the different phases of his life. In the initial stages as a composer we see a profound influence of North Indian classical music. Later in the second stage the classical structure of his compositions remained, but it was carefully fused with strains borrowed from the western music. Mostly old English ballads, Scottish and Irish country numbers were adopted as well. At this stage was born the 1st Indian opera of its kind the Valmiki Pratibha followed by the Kaalmrigaya and the Mayar-Khela.
The musical opera Kalmrigaya, describes the incident of the hunting by Raja Dashrath and the accidental killing of Sindhu Muni. Its two amazing songs in the last (6th) scene really touch the heart. Wish you will enjoy the recitation and songs! (Please forgive my faults, as I'm not a professional singer.)

The songs she sings are haunting and beautiful, even if I don't know the language.

Sorry, I know none of this helps, but it is interesting!