"Have you met Miss Jones?" was written for the 1937 musical "I'd Rather be Right". This was a collaboration between by the famous pair: Rogers and Hart who wrote 43 Broadway Musicals in all until Lorenz Harts death in 1943. Rogers continued with Oscar Hammerstein as his librettist to write many more great songs for the American musical theatre.
Certain historical and technical features in this song helped it become a Jazz standard:
It was featured by Sinatra in one of his best selling albums, was featured in the movie Bridget Jones' Diary, Ella sang it in her Rogers and Hart Songbook in 1957 and Joe Pass, guitarist, recorded it in his1973 album titled "Virtuoso" alternating playing it in F and Gb major. The song's bridge features key movements in major thirds and is thought to have have inspired John Coltrane to develop the "Coltrane Changes" or "Cycle" which are a series of harmonic progressions using substitute chords over common Jazz chord progressions.

In my arrangement of the bridge of this song I have followed the major third movements dutifully.