In the United States, most bishops are aware that lay people are not trained as they once were in ecclesiastical etiquette. If you greet a Catholic bishop, they will expect an informal handshake.
However, it can sometimes be confusing, as you may not always know what to call a bishop, or if there is some type of formal greeting that should be used.
In most cases, you can greet a Catholic bishop in this way:
Whatever you do, try not to get too nervous. Bishops are human. They are ordained to a special mission, but they are only in the place they are because of God.
There is a story of a young man at confirmation who accidentally called the bishop “Father.” Instead of rebuking him, the bishop said to the boy, “Don’t worry, that’s the best title I have ever had.”