Trump does not have basic good manners, so to expect him to know the finer points of etiquette protocol just doesn't make sense. Trump also has the reputation for caring only about himself.
It is disheartening to see some of the other replies to this question. Not all Americans are rude, ignorant about the finer points of etiquette, or history. To say that Obama was never criticized is ludicrous--realm after realm of news films filled with criticisms against Obama have been shown, over and over, on news casts. Americans do not have to bow to royalty--we fought a War of Independence and are a separate nation. Some Americans might do so, but they may be bi-national citizens of a monarchy and the US, or just don't known the proper behavior. An American may shake hands, accompanied with a nod of the head, to any one.