The local language in West Bengal is Bengali, and it comes in a gazillion different dialects and forms across the Indian province of West Bengal and the neighboring Bangladesh. It’s perfectly possible for people to grow up within 25 miles of each other and have a slightly hard time understanding each other. As a result, I only blend into the crowd as long as I keep my mouth shut (unfortunately, something that I’ve definitely had problems with in the past ^_^). You’ll find somebody almost everywhere who speaks English (though sometimes for a given value of English), so don’t let not knowing an Indian language stop you from visiting!
I should mention that India has something like 20 officially recognized languages and 900 local dialects—the only places on the planet that can compete in terms of diversity are Africa, parts of South America, and Oceania. Not to worry—English should get you by the majority of India, and with some supplemental Hindi you shouldn’t run into any insurmountable obstacles.
While I’m on the subject, I seriously need to do some studying. At my nebulous grasp of somewhere between 1 and 3 languages, I’m the dumbest of my relatives! Seriously- not a single cousin speaks fewer than 4 languages well enough to get by, and one uncle knows no fewer than 8! At 5 languages each, my parents are in the middle of the pack, despite how well educated they both are.