I decided to give it a shot and it seemed to me the song was in B. Might just be the Youtube version i got but it seems to me I've always heard the original in the same key this was in. Plus, understanding of horn players, piano players and jazz musicians of that era all suggest it would be B to me.

I let the bass player do a lot of the work. All I'm doing is vamping on the upbeats.

Over the first two lines of the verse I vamp on a Bar B dominant 7th, and do a dominant 9th over a F# and an F. Or B, B, F#, F, played as single downstrokes on the 'ands' or upbeats.

Your dominant 9ths are of course rooted off of the F# and F on your A string. So you are working up as the bass works down, forming a syncopated counterpoint as if you were horns.

Then on the third line of the verse follow the bass down, using straight barred dominant chords (No 7ths), vamping with downstrokes on the upbeats and when you get to F# hit it then bounce up an octave to your dominant ninth form and play F#, F.

And as everyone else has said swing it hard.