Of British-English origin, the phrase like the back (end) of a bus is used of a person regarded as physically unattractive or sexually undesirable.
The earliest occurrences of this phrase that I have found are as follows, in chronological order:
1-: From That Inferiority Complex, by the British psychiatrist Harold Dearden (1882-1962), published in the Sunday Pictorial (London, England) of Sunday 2nd December 1934:
What you want is to be so uniformly successful in a series of endeavours, that you will acquire at length the habit of expecting success in whatever you undertake. With this object in view there is nothing to compare with the formation of a resolve to do certain physical exercises at a fixed time every day. It is a task by no means impossible of achievement, and it is just boring enough to try out your newly fledged will-power and self-confidence. Incidentally, it will improve your general health.
With good health and the knowledge, born of this undramatic training, that when you make up your mind to do something you can do it, the world and all that is in it is yours, though your face be like unto the back of a bus.
2-: From Better Part of Valour, a short story by William Anthony, published in the Daily Herald (London, England) of Monday 29th June 1936:
He rang the bell, and James, his faithful valet for ten years, appeared.
“James,” he said, “you have done some odd things for me in your time, but this one will require every ounce of tact that you possess.”
“James, to-morrow I have arranged to meet a lady whom I do not know and have never seen in my life at the Ritz-Carlton.”
“I am afraid that I don’t understand, sir.”
“I will explain, James. This afternoon, while attempting to phone Paris, I became involved with a very charming voice, and so carried away was I that I went so far as to suggest making a rendezvous with the woman.
“Very foolishly, too, as I now realise, for she may look like the back of a bus.”
3-: From The Ashland Gazette (Ashland, Nebraska, USA) of Wednesday 6th January 1943:
Eddie Cantor * says that matrimony Is a 50-50 proposition alright. The husband gets 50c and the wife 50 bucks. Eddie knows slacks are the fashion for women but he continues to wonder why they wait until they look like the back end of a Greyhound bus before they start wearing ’em. A few more cracks like that and Eddie will find the front rows will be full of hard boiled femmes and what they will be throwing across the footlights won’t be flowers.
* Eddie Cantor (Isidore Itzkowitz – 1892-1964) was a U.S. entertainer.
4-: From the column In Hollywood, by the U.S. gossip columnist Erskine Johnson (1910-1984), published, for example, in the Miami Daily News-Record (Miami, Oklahoma, USA) of Monday 12th December 1949:
Film writer Ken Englund’s recent complaints here about movie cliches sent Parke Levy running to his typewriter. Parke is a radio writer—for the past three years head writer of the “My Friend Irma” show.
And, as everyone knows, radio is full of cliches, too.
But Parke isn’t.
“[…] [A] prime offender is what I call the adjective gag. A radio writer never describes a woman as just being stout. He resorts to a formula which invariably begins: ‘She is so stout that…’ (and the rest you fill in.) Such as:
“When she wears red earrings she looks like the back of a bus with the brakes on.”
Or, “—she has six chins—the last two are her stomach.”
5-: From The Essex Newsman-Herald (Chelmsford, Essex, England) of Friday 16th December 1949:
Career girls are making news. Take a look at these questions and answers in which (1) a married man and (2) a young woman endeavour to decide
WHEN CAREER GIRLS PREFER A HUSBAND
When a woman says, “I want to be a career girl, and don’t want to marry,” does she honestly mean it?
A. Of course not. Any girl with a career who is offered the choice of that or marriage will choose marriage. She becomes a career girl in the first place to earn enough money to make herself attractive to men.
If she genuinely prefers her career to the man, then the answer is that he is not the right one. When HE turns up, nothing will stop her.
P.S.: If she never gets married, she either has rotten luck or looks like the back of a bus.
6-: From the Fort Worth Star-Telegram (Fort Worth, Texas, USA) of Wednesday 4th October 1950:
Like the Back of a Bus—Oh!
English Girl on Cycle Says It’s Just Untrue
English girls don’t necessarily look like the backs of buses, a blond, curvaceous English girl traveling about the country on a motorcycle opined here Tuesday.
To back up her assertion, 24-year-old Toni Henly of Cheltenham, Gloucestershire, put herself forward as Exhibit A.
Toni had heard, she confided, that most Americans pictured a typical British pinup girl “as a horsy thing, wearing flat shoes and plain clothes and no makeup, looking something like the back of a bus.”