Born as Dorothy Tipton, she got into jazz in high school but was forbidden from joining the school band because girls weren't allowed. Because of this continuing pattern of prejudice against women in jazz, and because she liked getting it on with women, she began to dress like a man. At first it was just to fool people for jazz gigs, but she dug it so much that she completely became "Billy Tipton" and declared herself a member of the penis club. Sex change surgery being several decades in the future, Billy tied down his boobs and stuffed his pants.
Penis Club membership kit.
Incredibly, "he" got away with this through a long-term relationship with a girl. And then another one. And another. Tipton had five long term relationships in his life, and got by each time by claiming that a car accident had coincidentally mutilated both his man parts and his chest, which explained his chest bandages and why they always had to try unconventional sex methods.
A few close cousins may have known about his/her double life, and possibly some of his lovers, but you know who didn't?