Hello. What is the name of this movie: It was in black and white. A steamer carrying passengers had to be quarantined on an island. The main actors were a preacher/wife... sailor... a lady of ill-repute. Drums played in the background. I think William Bendix was one of the main characters... could be wrong. Thanks.

Miss Sadie Thompson

Since it's b&w, I'd go with the earlier film version:

Rain (1932)
Starring Joan Crawford, Walter Huston
TCM synopsis:
A ship docks in rainy, tropical Pago Pago, discharging among others, Alfred Davidson, a self-righteous missionary, his prim, proper wife, and Sadie Thompson, a woman with an unsavory background. Sometime later, a cholera epidemic forces them to remain quarantined on the island, and Davidson decides he will reform Sadie and save her immortal soul. When she spurns his offer, Davidson has the governor order her deportation to San Francisco. She begs Davidson to allow her to remain a few more days, so she can sail to Sydney, Australia instead, but during the argument, she experiences a religious conversion and agrees to return to San Francisco and the jail sentence that is waiting for her there. The evening before she is to leave, Sergeant "Handsome" O'Hara, who has fallen in love with Sadie, asks her to marry him and offers to hide her until the Sydney boat sails, but she is under Davidson's spell and refuses. Later, while native drums beat, Davidson succumbs to her beauty and accosts her. The next morning, he is found dead, a suicide. Now disillusioned with Davidson's teachings, Sadie becomes her old self and plans to go off to Sydney with O'Hara to start a new life.

From TCM:
Previously filmed as "Sadie Thompson" then again as "Dirty Gertie from Harlem, U.S.A." and "Miss Sadie Thompson".

Rain (1932) - Overview - TCM.com