Green’s Dictionary of Slang

(US) to stare.

1955		‘Blackie’ Audett Rap Sheet 97: He was craning his neck and bug-eyeing the door.
1957		‘Ed Lacy’ Lead With Your Left (1958) 43: I must have been giving her bug eyes for she glanced down at herself.
1969		‘Iceberg Slim’ Pimp 114: The couples in the booths were bug-eying the arena.