The Bullitt Charger was an automatic. You can see the shifter in one of the scenes. Bonus points, though for being the first person in this thread to spell Bullitt correctly, though! :-)
It was definitely a 4 speed ; one can see not only Hickman's shifting prowess on the curved hill at the beginning , but also the (stupid,cheap) Inland Shifter knob .
I'll post the vid of the chase ...