This phrase is widely attributed to Gloria Steinem, the implication being that many women may well have no need for or even use for men. The humor derives from the fact that sexual and lingustic stereotypes make the brain expect to hear 'water' as the last word.

A web site called The Phrase Finder at quotes from a letter sent by Gloria Steinem's letter to Time Magazine in autumn 2000. Part of her letter is quoted below.

"you credit me with the witticism 'A woman needs a man like a fish needs a bicycle.' In fact, Irina Dunn, a distinguished Australian educator, journalist and politician, coined the phrase back in 1970 when she was a student at the University of Sydney."