A bomber station is a small white trailer located near a central objective in Conquest on China Rising maps where you can press X to send out a bomber. A camera will zoom up to a bomber plane which you'll then be gunning from.
Find a target with the action button (default is RB) and then paint him with the right trigger. You'll get three bombs before a long reload, so place them well. I got this first try by targeting snipers camping on a hill.
Note: According to commenters, killing players inside vehicles does not count towards this, but aiming at vehicles may earn you stray infantry kills if you can't find any.