Your link doesn’t show anything because you put quotes around “bump and grind” so ngrams looks for the phrase with quotes. That’s different from almost every other search engine, including Google. You also start the search with 1950, which is way too late.
But the 1940 and 1941 links in posts #6 and #15 are to Google Books, so it’s certain that the phrase is older than 1957. And references from the 1950s are plentiful.
Love and Mrs. Candy - Page 19
Robert Tallant - 1953 - Snippet view
“Henry, why don’t you get Noonie Belle an aspirin to take with her beer,” she suggested. “I don’t want no aspirin,” said Noonie Belle. “My head don’t hurt. Look, I gotta idea. Do you think Philandra Fazende would give me some lessons? I mean in dancing and stuff like that. When I met her on Cairo Street one day she told me how she used to be a big star.” “Miss Fazende has imagination,” said Mrs. Candy quietly. “I can do a bump and grind,” said Noonie Belle, "and I can do cartwheels.
Saturday Review - Volume 36 - Page 28
1953 - Snippet view - More editions
… was evidently not fully sure that Miss Monroe and Miss Russell could dance — really dance, that is — so he has mainly kept them to burlesque-type routines. To learn these, the vital statistics continue to inform us, the girls were sent to some downtown Los Angeles burlesque houses to pick up what pointers were needed. There they quickly learned how to parade, bump, and grind. However, censorship codes protect us from the true parade, bump, and grind of the burlesque show.
Fortnight: The Newsmagazine of California - Volumes 10-11
1951 - Snippet view - More editions
The B**ump and Grind Business **First of a Series Explaining Why Burlesque Is Becoming Los Angeles’ Major Entertainment CIVIC AFFAIRS The Europeans By Clement Reicher PEOPLE BUSINESS, INDUSTRY. Only 18 short months ago there was one burlesque theatre in Los Angeles. At last count there were three theatres. 23 nightclubs in the County featuring strip shows and new shows mushrooming each week. While the more sedate members of show business refer to this trend …
Time - Page 34
Briton Hadden, Henry Robinson Luce - 1952 - Snippet view - More editions
It was heaped high with a weird mixture of pornography, childishness and sentimentality — mild glamour shots like those advertising Chicago burlesque bars: Kodachrome nudes complete with pocket viewers; trick photographs that could be squeezed to make a fan dancer bump and grind. There were also pictures of Queen Narriman as a bride. Near the royal bed stood two stacks of well-thumbed U.S. comics. In the dressing. room were 100 suits. 50 canes. 75 pairs of binoculars and …