From the Routledge Dictionary of Historical Slang:
Bread-and-butter: 1 Boyish, girlish, esp. schoolgirlish, as in a bread-and-butter miss: coll; from ca 1860.
The origin is not explained, but I think you can safely forget about it unless you are making a study of antiquated expressions. This expression fell into disuse through the twentieth century, and I don't think anyone would use it today.
We do still use bread and butter to denote dull things in some contexts, in the UK. You might see it used to describe something as routine, unimaginative, but I have never seen this collocation with "miss" and would find it very odd if I read it in a modern text.
Per suzi's post #6, in AE we also currently use, very much so, "bread and butter issues" as a political term, something with deep economic implications for voters struggling with varying policies affecting their jobs and salaries, so therefore the ability or lack thereof to feed their families, etc.