Do biceps get trained when you only do the big three (squats, deadlift, bench)?
The absolutely do! The biceps are an antagonist (meaning provide opposing force) on the bench press, on deadlifts the biceps actively contract as you grasp the bar and on squats the biceps work to stabilize the bar.
However, if looking to maximize results, even the greatest powerlifters in the world include accessory work in their program. Accessory work would be strengthening the individual muscles involved in the Big 3 movements. This addresses potential imbalances and also helps power through sticking points in the lift, such as the middle of a bench press (this requires a lot of triceps activation, which can be addressed through accessory work).
Here is a great example powerlifting program that includes accessory work: 5 Day Powerlifting Split - 16 Week Long Term Meet Prep
Best of luck building those big biceps and getting as strong as possible!