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Originally and chiefly U.S., the expression bag stuffer designates an advertising leaflet or similar piece of promotional material handed out to shoppers or placed in shopping bags alongside goods purchased.

This expression occurs, for example, in the following from Red Cross and Acme Join In Blood Donor Campaign, published in the Citizens’ Voice (Wilkes-Barre, Pennsylvania, USA) of Thursday 17^th December 1981 [page 18, column 1]:

Wilkes-Barre Mayor Thomas V. McLaughlin kicked off recently a cooperative effort between the American Red Cross and the Acme food store chain to reach 400,000 prospective blood donors during the last two weeks in December.
Four hundred thousand is the number of grocery bag stuffers the Red Cross has supplied to Acme stores in the Wilkes-Barre/Scranton area. The bag stuffer consists of a Red Cross flyer listing the time and place of all area bloodmobiles scheduled through the end of the year.

These are in chronological order, the earliest occurrences of the expression bag stuffer that I have found:

1-: From Avoid Child Traffic Accidents, published in the Detroit Tribune (Detroit, Michigan, USA) of Saturday 13^th May 1950 [page 4, column 5]—here, the expression is shopping-bag stuffer:

Prevention of child traffic accidents, which always rise sharply during spring, is being stressed by Detroit safeay [sic] agencies in a city-wide program which started last Monday and contines [sic] until end [sic] of the school year.
Enlarging the scope of the program will be major chain grocery stores and neighborhood indendents [sic], who will carry on a number of activities designed to impress parents with the problem. These activities include newspaper advertisements, store posters, shopping-bag stuffers and public address announcements in stores.

2-: From Wednesday, Thursday—Kiwanians Schedule Auction, published in the Geneva Daily Times (Geneva, New York, USA) of Tuesday 28^th June 1955 [page 9, column 2]:

PENN YAN—In an all-out community drive to help in youth projects, the Kiwanis Club is holding a two-day Do-Good Auction Wednesday and Thursday at Grange Hall, W. Lake Rd.
Four loads of household furniture are included in the hundreds of items which will pass over the auction block to the highest bidders. Four used cars, all in mobile condition, are ready to go.
[…]
[…] Local merchants have cooperated with the move and in many stores, printed lists of the items have been used as “bag stuffers” to be put in every package or given to each customer.

3-: From Lovett’s Food Stores to Push Fruit and Juice, published in the Vero Beach Press-Journal (Vero Beach, Florida, USA) of Thursday 7^th July 1955 [page 4-A, column 5]:

Lovett’s Food Stores will join other members of the National Association of Food Chains in a “Summer Citrus Coolers Campaign” to boost consumption of canned grapefruit sections, lemonade and limeade […].
Besides the three main items, the campaign will feature frozen grapefruit sections, lemon juice, fresh lemons and fresh limes. Special attention will be called to the citrus campaign in Lovett’s 72 stores through advertising, store displays, bag stuffers, and direct mail.

4-: From Upping Shop-At-Home Ratio Is Goal Of Spring Campaign, published in The Irving News Record (Irving, Texas, USA) of Thursday 7^th February 1957 [page 4, column 3]:

An energetic citywide merchandising promotion designed to boost Irving retail sales during the spring and Easter season planned by the trade extension committee of the Irving Chamber of Commerce was adopted Tuesday. […]
[…]
The program [was] worked out by the committee through assistance from the Irving News. […]
The News is providing at no cost to participating merchants 600 window placards, 20,000 bag stuffer circulars, 1000 store banners and will carry out the Easter Egg contest in the News and advertising columns of the News.

5-: From an advertisement for De Soto Tom-Boy Market, published in The Jefferson Republic (De Soto, Missouri, USA) of Thursday 21^st February 1957 [section 2, page 2, column 7]:

Be sure to ask for your money-saving “bag stuffer” on next week’s De Soto Tom-Boy’s “PENNY SERENADE”