Ululation is of such ancient origins, likely in Sumer, that it would be difficult to trace its diffusion to other cultures.
For example, a Sumerian proverb written down 4,000 years ago reads:
(What characterizes) the carpenter is the chisel
(What characterizes) the reed weaver is the basket
The blacksmith (is known to) make tiny sides
(What characterizes) the professional singer is ua alala
In other Sumerian texts, phonetically similar terms could be used to indicate joy or woe, just as ululation does in modern cultures. For example, joy:
alliliamma--in the house--ulili! Pour out for him beer there, pour out
for him wine there there Oh sukkal, pour out wine there for your lord!
He said alala when he broke the punting-pole
Ululation had already diffused widely by around 3,000 years ago. The ancient Egyptians ululated, as did the ancient Greeks who called it ololugê. Ululí-ululú is Sanskrit for 'howling' and ulult is "an outcry indicative of prosperity." Hebrew has terms like layalel and yelalah that indicate lamentation. All of these terms predate the Latin ululāre, from which the English and Romance terms for ululation come form.
As for the Indian subcontinent, Wikipedia indicates that ululation is "widely practiced in eastern parts of India," as well as some southern regions and West Bengal. The Sanskrit ululí-ululú is similar to the modern Bengali term ulu-uli, the modern Oriya term Hulahuli, and the modern Assamese term uruli.
My source for all of this is a 2008 dissertation, "Ululation in Levantine Society", by Jennifer Jacobs. Her review of the literature suggests that very little has been written about ululation, at least not in English. So I'm doubtful how much more information can be dug up on the migration of ululation from Sumer to Bengal (again, at least not in English) since that migration likely happened so long ago.