What is a good bicep workout
Bench press and push-ups work the triceps and shoulder parts of the arm, not the biceps. If you are looking for compound movements that incorporate the bicep muscles, then go with chin-ups, lat-pulldowns (preferably under-hand grip), bent-over rows and T-Bar or seated rows. If you want to isolate the bicep muscles, I would recommend concentration curls, preacher curls (with a curl bar), and hammer curls (these also work the brachialis muscles). On any given day I only do 3-4 sets of isolation exercises for the biceps because doing too many curls and focusing too much on single muscles will make lead to disproportionate muscle growth and appearance.
Pull-ups certainly help, but the other two are for chest, shoulders and triceps. I would still recommend those anyway because you never want to focus too much attention on single muscles :).