The Gentleman's Magazine Library - Dialect, Proverbs and Word-lore (edited by George Laurence Gomme) says that bumfiddle might be a corruption of the term bound-bailiff but doesn't include the source of the corruption:
The learned author of the " Commentary on the Laws of England" has clearly shown (b. i. c 9, 8vo. edit, p. 346) that another word, to which the same monosyllable is now usually prefixed, has suffered an alteration by the common people; for that " bound-bailiff" was the original term : and possibly this may have been the case in the word before mentioned, though I am not deeply enough versed in antiquarian lore to discover the source of the corruption.
However, according to OED, the noun bumfiddle, meaning bum, is from 1675 and the noun bound-bailiff is from 1768. Thus, the vulgar meaning bumfiddle might be earlier than the non-vulgar meaning.
OED defines bound-bailiff as a name given by Blackstone to the sheriff's officer in explanation of the vulgar term bumbailiff:
The sheriff being answerable for the misdemesnors of these bailiffs, they are therefore usually bound in a bond for the due execution of their office, and thence are called bound-bailiffs.
1768 W. Blackstone Comm. Laws Eng. I. 346
OED defines bumbailiff as a contemptuous synonym of bailiff which means an officer of justice under a sheriff, who executes writs and processes, distrains, and arrests; a warrant officer, pursuivant, or catchpoll.
According to OED, the etymology of bumbaillif is apparently < bum + bailiff : i.e. the bailiff that is close at the debtor's back, or that catches him in the rear. Compare the French equivalent pousse-cul , colloquially shortened to cul, precisely like the English.
The Routledge Dictionary of Historical Slang (by Eric Partridge) says that the derivative bumfiddler, meaning a fornicator, is from 17th century and rare. Here is the excerpt of the definition of bum-fiddle:
A Dictionary of Sexual Language and Imagery in Shakespearean and Stuart Literature (by Gordon Williams) includes different slang meanings of bumfiddle in different works. It says that the term is a slippery one ranging from bum to bumbaste. The term is also used for coital and vaginal sense. You can read further in Google Books.
Another similar term is bumfeagle which also means bumbaste: to beat on the buttocks (dialectal, England). [MW]
Here is the excerpt from The Routledge Dictionary of Historical Slang: