Bottomless Cup

A “bottomless cup” of coffee means that the establishment offers free refills of coffee. The coffee cup has a bottom, of course. The term “bottomless cup” dates to at least 1934 and appears to have been popularized by the B/G shops at Chicago.
 
Many restaurants offer free refills of soda, but the term “bottomless glass” hasn’t been used.
 
   
16 November 1934, Chicago (IL) Daily Tribune, pg. 5 ad:
...bottomless cup of coffee for a thin dime…
 
9 January 1935, Freeport (IL) Journal-Standard, pg. 5, col. 4 ad:
T-Bone Steak Supper
(...)
And a
Bottomless
Cup of
Chase & Sanborn
Coffee
Ford Hopkins Co.
 
Google Books
December 1936, The Fourth Church (Fourth Presbyterian Church, Chicago, IL), pg. 292, col. 2 ad:
It’s a BOTTOMLESS cup at B/G always.
640 NORTH MICHIGAN AVENUE
   
18 June 1940, Marietta (GA) Daily Journal, pg. 4, col. 7 ad:
COFFEE
Makes the Meal
THAT’S WHY WE SERVE THE BEST IN TOWN
Bottomless Cup at
DIXIE CAFE
 
24 October 1940, Mason City (IA) Globe-Gazette, pg. 14, col. 1 ad:
BOTTOMLESS CUP OF COFFEE (Always)
(Walgreen Drug Stores—ed.)
 
Google Books
30 November 1942, Life, pg. 68:
(Sign: “COFFEE RATIONING…Due to rationing we will be unable to serve more than ONE CUP of coffee per guest.”)
Placards like one above have been up for some time in “B/G” chain of restaurants. Before April they featured the “bottomless cup” or all that one could drink for 10c.
 
7 June 1949, New York (NY) Times pg. 4 ad:
B/G Good Food Restaurant
23 William St.
Famous for the “Bottomless Cup” of B/G Coffee…from Coast to Coast.