Green’s Dictionary of Slang

1. (US) circumstances, situation.

1937		P. Cheyney Dames Don’t Care (1960) 64: While I am flying back to Palm Springs I think out how I am goin’ to handle this bezusus.
1939		P. Cheyney Don’t Get Me Wrong (1956) 46: Some bozo [...] who can throw a spot of light on all this bezesus.

2. a person; thus Big Bezezus, an important man.

1930

M. Allingham Mystery Mile (1982) 352: It also gives us the blessed possibility that the Big Bezezus himself will turn up to make a personal affair of it.