Who is the female actress who grew up in Washington state and played part of Mame?

You're likely thinking of Bea Arthur.

While she is most famous for her role as Maude Findlay, she also originated the role of Vera Charles in the musical "Mame", which opened in 1966.

While Bea Arthur was born in New York, she did grow up in Camden, New Jersey, not Washington State.

Perhaps you are thinking of another actress who played a role in a different version of "Mame" or a different show entirely. Could you provide more details?