Cindy-If you wish to adhere to the definition of "bush league" then the only legal shot I can think if that fits the definition is the underhand serve.
I suppose certain styles of play you see at the rec level could be considered bush league. For instance, I have never seen a pro serve with a frying pan grip/style, but rec players often do.
Frying pan serves are also therefore "bush league."
Btw, I saw a video of Sharapova hitting an underhand serve. She looked to be injured or cramping. Same for Chang. Which supports my answer to OP's question of whether underhand serves from unimpaired players is bush league.
By all means, serve underhand if you like. I will try to win the point and will not be angry or upset. I will simply conclude you are bush league.
I typically find your reasoning to be extremely logical and generally well-reasoned even if I don't necessarily always agree but I have to say that I'm not following you here at all.
Are you actually saying that hitting a serve underhand, in and of itself, is bush league or is that sometimes, when people serve underhand, they do it as a sort "quick serve" trying to get the serve over before the receiving player is ready.
I would agree that quick-serving someone before they're ready is bush league but catching them off guard by throwing in something unexpected is just strategy.