You can probably never completely do away with anti-Americanism or anti-American bias, as there is sentiment against every nationality. However, there are several PODs which would greatly reduce it:
1. Get rid of America: Rome discovers and colonizes America, and either lasts perpetually or breaks up later than it did in OTL. As a result, America experiences a Classical and Medieval Age, as well as a rennaisance. Of course this would require the Romans to have much better seafaring tech than they did in OTL, when it wasn´t until 1434 that a European navigator rounded Cape Borjador (a protrusion on the coast of Morocco). A Roman America would also butterfly away almost all of history as we know it.
2. Get rid of American exceptionalism. This grates on the nerves of non-Americans to no end, and is the cause of much of the self-righteous rhetoric of American politicans, as well as the perception that Americans are arrogant. However, American exceptionalism is so deeply ingrained in American culture that it´s difficult to imagine it without it. For American exceptionalism to not exist, the american revolution would probably have to fail, which would create an America and a world very different than the one we know.
3. Get rid of the Cold War: the conduct of the United States during the Cold War, as well as the efforts that the USSR, Cuba, and leftist intellectuals worldwide dedicated to discrediting the United States and publicizing its worst traits and actions, are responsible for much, if not most, of the anti-Americanism in the world. Maybe Britain wins Gallipoli, World War I ends in early 1917, and the British Empire remains top dog into the 22nd century. Maybe stalin rather than FDR dies in April 1945. That might be all it would take for the cold war to not arise, or at least to be much less cold.