The Bodleian Library has a copy of "Unfortunate Miss Bailey" with an illustration showing Captain Smith, in his bed and holding his libation, and Miss Bailey (looking quite substantial) remonstrating with him.
The sheet was produced by Laurie and Whittle, London, Feb. 12, 1804, and states that it was sung in the play by Mr. Matthews at the Haymarket (Theatre) and Mr. Fawcett at Covent Garden.

The third verse differs in the first line from that in the DT:

Avaunt, Miss Bailey, then he cry'd. "your face looks white and mealy."
Dear Captain Smith, the ghost reply'd, "you've used me ungenteely.
"The Coroner's quest goes hard with me because I've acted fraily.
"And Parson Biggs won't bury me, tho' I am dead Miss Bailey."

"Dear Corpse," says he, "since you and I accounts must once for all clear close,
"I've got a One Pound Note, in my Regimental small clothes,
"Twill bribe the Sexton for your grave." the ghost then vanish'd gaily,
Crying "bless you wicked Captain Smith, remember poor Miss Bailey."

(At the time, one pound was a fair sum; versions citing ten pounds are modern adaptations.)
I haven't found the source for the fifth and sixth verses.

http://www.bodley.ox.ac.uk/ballads/ballads.htm