What is the meaning of the idiom to grow a funny bone? What does funny bone refer to? Googling shows only places where it was mentioned.
I've never heard the whole expression as such, but it can be broken down in to two common idioms:
funny bone: a sense of humor.
"Grow [something]" : You lack [a personality trait represented by that thing]. In particular, it's used as a sarcastic criticism of the person, suggesting the person would benefit by having more of it.
A fairly common usage is the phrase "Grow some balls", with balls meaning testicles, and thus courage or fortitude.
So "Grow a funny bone" means "You don't have a sense of humor". You might say it if you make a joke and someone gets unreasonably offended by it.
The "funny bone" is the nickname for "a long bone in the arm or forelimb that runs from the shoulder to the elbow", whose technical name is the humerus. I think it is fair to say that the nickname is based on a play on words (i.e. Humerus/Humerous), although my mother always maintained it was "funny" because it sends tingles up your arm in a funny way if you knock it.
According to Google N-Grams, this nickname has been in popular use since the early 19th century.
The phrase "Grow a funny bone" is not one I've come across before, but I think it is safe to say that it must mean:
"Get a sense of humour"
A quick look again at Google N-Grams suggests that it is certainly not a common expression(!)
I wonder where you heard it, and whether the person who told you it had made it up themselves.