Copied from elsewhere on the internet......
It appears that the 1960s was when the term began being used to
describe cover for a homosexual male.
"Lets look at the gay slang term beard, which, according to the
Dictionary of Gay Slang, originated in the mid-60s and is used to
describe a straight woman married to or involved with a gay man. The
gay man may be in the public eye, and may have a beard to hide the
fact that he is gay.
From The Return of the Hirsute ****
By Michael Svoboda
Mid 1960s date also confirmed here
OTHER LINKS THAT MAY BE OF INTEREST
"According to gay slang and The A-List, a merkin is defined as "a man
who dates or marries a gay or bisexual woman so that the woman can
pretend to be heterosexual". Conversely, a beard is "a woman who dates
or marries a gay or bisexual man so that the man can pretend to be
heterosexual".
"FOD = Friend of Dorothy or Gay Male
Bi___________ = Bi Sexual
L____________ = Lesbian
Merkin is a Man who is married to a bi women or lesbian women.
Beard is a women married to a bi or homosexual male."
Forum post at the A-List
EDIT
"Beard, "A person of the opposite sex, either heterosexual or
homosexual, who knowingly dates or marries a closeted lesbian or gay
man to provide that person with a heterosexual `disguise', usually for
family or career purposes."
"beard Noun. A woman who is seen to be romantically linked with a gay
man, so protecting his true sexuality from public scrutiny - often
associated with celebrities. [Orig U.S.]"
One of the general definitions of beard is "One who serves to divert
suspicion or attention from another," and that has been used for many
years - beards are grown to cover.