Of American-English origin, bag lady denotes a homeless woman, often elderly, who carries her possessions in shopping bags.

The earliest instance that I have found is from Jack O’Brian’s column New York’s Voice of Broadway, in The Pocono Record (Stroudsburg, Pennsylvania) of 19^th June 1971; the author paid tribute to Joe E. Lewis (Joseph Klewan – 12^th January 1902–4^th June 1971), American comedian and singer (bumb apparently denotes a homeless person):

Joe E. had a far more sensitive perception of what made people smile than his raffish midnight companions believed… He remained loyal to certain cerebral clownings that escaped rowdier guffaws; these Joe would deliver and upon the imperfect tribute of silence, would comment through the collective shrugs, “That joke doesn’t get a big laugh—just intellectual nods”; and he was right; it also was one of the reasons his fans ranged from the bumbs and bag ladies all the way up to pedants.

The second-earliest instance that I have found is from the column Buzz of the Burg, by Ing, in the Idaho State Journal (Pocatello, Idaho) of 31^st July 1972; the author wrote about Sharon Curtin, author of Nobody Ever Died of Old Age (Little, Brown and Company – Boston, 1972):

Indignant at the way American society isolates and ignores its old people, sickened by our waste of their talent and experience, Sharon Curtin creates a series of striking portraits: her beloved, rugged grandparents; a “bag lady” who skulks through New York carrying all her earthly possessions; two tough old men who taught her their skills.

The earliest instance of the variant shopping-bag lady that I have found is from The Arizona Republic (Phoenix, Arizona) of 3^rd June 1973:

Thief misses $42,000 in fatal attack

Associated Press
New York—A 70-year-old woman, known by Times Square regulars as the “shopping bag lady,” was found stabbed to death in a public restroom in her hotel yesterday with $42,000 in travelers checks pinned to her underwear, police said.
The woman, Belle Gretzner, was discovered by a hotel maid lying in a pool of blood just inside the door of the ladies room, police said.
They said the probable motive in the killing was robbery, but that the murderer had missed a bag of travelers’ checks in $100 and $500 denominations that she had concealed in her clothes.
Albert Rothenberg, night manager at the Times Square Motor Hotel, said the woman had lived there for 3½ years and that little was known about her except that she was a retired schoolteacher.
She was known as the “shopping bag lady” because of the two shopping bags, crammed with all her known possessions, that she carried with her wherever she went.
Rothenberg said Miss Gretzner never received mail at the hotel, but picked up her pension checks at a private post office box.