The song Birthday was written and recorded on the same day, Wednesday 18th September, 1968 at Studio Two, EMI Studios, London. The Beatles took a break from recording at the Studios to go to McCartney's house with Yoko Ono, Pattie Harrison and Chris Thomas and probably others to watch the 1956 Rock and Roll film classic That Girl Can't Help It which was being shown on TV. Inspired by seeing Eddie Cochran, Little Richard, Gene Vincent, Fats Domino and others in the film, they then returned to the studio and did their own version of a 1950s hit which was Birthday. According to Lewisohn ...Paul had concocted the new song earlier, right there in Studio 2. When they all returned energised by the film ...'Birthday' was finished off with a four-track to eight-track copy and a host of overdubs onto this: tambourine, piano, handclaps...backing vocals...and Paul's lead vocals with occasional contributions from John....

It would appear from these notes that Paul abbreviated the line I would like you to dance....to Do You Want To Dance as a form of shorthand.