One of the verses has the lines "Go upstairs and put your glad rags on / And join me, hon, and we'll have some fun." At first, I recognized just the phrase "glad rags," but when I verified the source, I discovered that there's a substantial similarity between these two lines and the first two lines of the first verse of Bill Haley & His Comets' "(We're Gonna) Rock Around the Clock": "Get your glad rags on; join me, hon / We'll have some fun when the clock strikes one." Aside from a few minor differences, these two pairs of lines have the same three clauses: "Get/put your glad rags on," "Join me, hon," and "We'll have some fun."
These lines are so similar that I don't think it's just coincidental. I'd find it hard to believe that these lines in "Saturday Dance" weren't intended to quote "(We're Gonna) Rock Around the Clock."
I did some research and discovered that "(We're Gonna) Rock Around the Clock" was written by Jimmy De Knight and Max C Freedman and came out in 1954. The publication data of my 3-CD Shadows set credit "Saturday Dance" to "Chester/Marvin" (I'm assuming "Marvin" is the Shadows' Hank Marvin) and note that it was recorded in 1959. There are five years between the two songs, so chronologically, it's entirely possible that "Saturday Dance" quotes "(We're Gonna) Rock Around the Clock."
The bass part for "Saturday Dance" sounded pretty easy, so I figured it out and notated it. I should note that my notation starts at the same time the bass part starts. At the very beginning of the song there are a few measures comprised solely of guitar, but I didn't include those. And, as always, there's the disclaimer that I might have something wrong:
