Can anyone help me that how long does it takes travelling by bus from Washington DC. to New York?

I can't vouch for buses, but in a car it's a four hour easy drive . .. .. . assuming one rest stop for comfort and no traffic problems (no rush hour, no construction or accident delays, etc.). . Assuming you come up I-95, you have Philly traffic and NY bridges to deal with, so there never is any guarantee. Good luck!