What Do Bishops Normally Wear?

Their vestments are called cassocks. The inner cassock is simply called a "Cassock". The outer cassock is called a "ryasa (russian) or "exorason". A "skufia" is a soft sided cap. A "kamilavka is a stiff hat. An "epanokamelavkion" is a veil extending over the back, worn with the kamilavka by all monastics and bishops. A "klobuk" is a kamilavka with an epanokamelavkion permanently attached; more common in the Russian tradition. (I just came up with that off the top of my head.)

Well all I know is that when he goes somewhere he brings his staff with him, he a busy fellow, and his head wear is called a Miter because it has a sharp angle on top.  I also know he has money because a lot of it is in vestments. If he is traveling to the Holy land he also wears a purple Yarmulke.

In their private living quarters, they wear slacks, shirt and tie.

They tend to were casual dress wear in public.
Other then their alter gowns

ALL priests or bishops wear a white cloak over thier regular clothes.  Just like Superman does. He wears his Clark kent clothes over his uniform.

An Anglican bishop wears a cloak called a Cope, and a hat called a Mitre. He also carries a shepherd's crook.