In the 4/4 time signature, which may be over 95% of popular music today, dancers count beats in "sets of 8" also known as the "8-count" or the "dancer's 8." Musicians count in measures of 4 beats. The two systems are different but related and can coexist (although some musicians have never heard of the 8-count so they might argue that point).
In a lot of 4/4 time music, two 4-beat measures will be rhythmically paired, which is what creates the 8-count. If you listen closely, an 8-count will sound like a "sentence" of music, which makes it an easier structure to work with when choreographing dance. I write about music and dance and to quote from my book, Hear the Beat, Feel the Music: Count, Clap and Tap Your Way to Remarkable Rhythm (ihatetodance.com): “Sets of 8 are a dancer thing. They’re better for identifying the structure in popular music, which you need for choreographing movement, a moot point to a musician. Sets of 8 are better for predicting where the music is going, whether you’re a dancer or just a person who enjoys listening to music.”
I don’t know the origin of the 8-count, so I can’t give you a historical perspective. But I just spoke with dance educator Skippy Blair, who was born in 1924, and she said she was working on sheet music for a band in the 1940s (when she was a teenager) and she was using the 8-count. She believes that the 8-count dates back earlier than 1900.
I would like to correct your language. A “bar” is slang for “measure.” In 4/4 time, bars are 4 beats of music. So the concept of an “8-count bar” is erroneous. An 8-count would be 2 bars of music (8 beats). It looks like this (note that, in the musician’s count, count 1 of the second measure is the same as count 5 in the dancer’s count):
1234 5678 – dancer’s count (an 8-count)
1234 1234 – musician’s count (two 4 beat measures)
I use the terminology of Skippy Blair (swingworld.com) and refer to an 8-count as a “mini-phrase” of music (four sets of 8, which is 32 beats of music, is called a "major phrase," and is probably the most common phrasing in popular music today). In my experience, a musician would refer to an 8-count as just a “phrase” of music (I also think they would call the 32-beat major phrase just a "phrase" of music--but I'm open to be corrected on this). I’m making a point of language because the dancer’s count and music theory can coexist, but it’ll get confusing if we blur the language.