This phrase is used when something difficult needs to be done, usually at the expense of someone's feelings or efforts. For example, if you need to end a relationship and no matter what you say or do will be the right way to do it. It doesn't matter if you wait until after the person's birthday, or do it just before their birthday, it just seems like "there's never a perfect moment" to do it.
You hired a friend to work for you, but now you need to fire them. There is never a perfect moment to tell them.
You're moving out of the house, but your mom is very close to you. Even though your new place is great, your mom will not understand, so there will never be a perfect moment to tell her.
These are how I see your examples:
A) Incorrect. To never do it is actually not the solution. It still needs to be done somehow.
B) Correct. But it's: "There's never a perfect moment to do something" (do not use "there's is" together).