Short Answer:

No the bench press does not work the bicep musculature.

What Muscles Does The Bench Press Work?

The bench press is a horizontal press movement . The horizontal press movement is predominantly uses the muscles of the pectoral's and triceps, but also includes stabilising muscles of the shoulders and the anterior deltoids. The bench press should not be considered an exercise that will create an adaptation in the bicep muscles.

What Exercises Do Work Biceps

No we are aware that the bench press does not work the biceps, which exercises do? There are multiple ways to work the bicep muscles, some more direct than others.

Bicep Isolation Exercises

Bicep isolation exercises are the most effective way to improve the size and strength of the biceps, through using exercises which specifically isolate them. Below are three examples of bicep isolation exercises.

Horizontal Pulling Exercises

Horizontal pulling is a less direct way to work the muscles of the biceps, but will still have an impact on the strength and size of your biceps. Personally I would not include these in your bicep weekly volume if you are training to grow your biceps. Below are three examples of horizontal pulling exercises that you can use to work your biceps.

Vertical Pulling Exercises

Vertical pulling exercises are also an effective way to work your biceps. Anyone who can perform 20+ strict pull ups will likely have very strong biceps and may not even do any bicep isolation work. Pull ups are the most effective exercise to grow the biceps in the vertical pulling movement category.

Effective Programming for Growing The Biceps

In order to grow the biceps you need to be performing 8-15 working sets per week in order to see progress. This depends on your training age, a beginner will see huge benefit with just 8 whereas someone who is very advanced may need 15-20 sets per week to see progress. I would only include the bicep isolation exercises in your working sets and not the pulling variations discussed above.