Often with reduplicated phrases there is a source word which conveys the meaning and this is added to by another word or words. The subsequent words don’t have to make sense, they are there for rhyming, repetitive or alliterative emphasis.
In bish-bash-bosh it is bash which conveys the ‘sudden, vigorous blows’ meaning. Bish didn’t exist as a word in itself when this phrase was coined. Bosh has many different meanings but none of them fit with this phrase – apart from the recent ‘sudden, effortless happening’ meaning, which is just a shortening of bish-bash-bosh and not the source of it.
Two meanings given above probably derive from the same thought. The meaning of the expression could be widened to ‘things were like this and then, all of a sudden something happened, and they were like that‘. That could refer to a rapid flurry of punches or to any other sudden happening.
Early examples of bish-bash-bosh in print come from the USA and don’t make it clear which meaning was intended. The earliest I know of is from The Kansas newspaper The Daily Independent, May 1903, in a report of a debate between two groups of students:
While waiting the decision of the judges… a bunch of bright young ladies from the Philomathians cried out in loud tones:
“Bish, bash, bosh, bish, bash, bosh, you old Athenians take it in your wash.”
[Note: There is an example of ‘bish-bash-bosh’ in print from the early 19th century. This is in a bizarre dictionary called the Etymologicon Universale, 1811. The book is based on the nonsense theory that only consonants contribute to the meaning of words and that vowels are irrelevant. That theory would consider bish, bash and bosh to all be the same word. The placing of them together in the book seems to be random chance and not a meaningful usage of the phrase bish-bash-bosh.]
Following the 1903 example the phrase wasn’t widely used. There are a few examples of it from both the USA and UK. In 1960s UK it was used with the ‘sudden blows’ meaning in a description of stage fencing technique.
It wasn’t until the late 1980s that bish-bash-bosh began to be used more commonly. In the UK this was as a result of the catchphrase of Loadsamoney – the loud-mouth yuppie plasterer character created by Harry Enfield:
“Bish bash bosh, look at my dosh”
The phrase was taken up in Britain and then appears to have migrated back to America with the ‘easy, quick transformation’ meaning.