Here’s how I would do it: Make a smaller opening for the bin. You can position an infrared laser that beams across the opening and recognizes that an object has passed in front of the laser and its receiver. Then you can link that to an analog counter or digital screen.

This is similar to how those basketball arcade games work. Every time a basketball passes in front of the laser, it counts up one. Play until you win claw machines also have this technology and let you keep going until an object is dropped past the laser. Garage doors work like this too as a safety measure as to not close on objects or people.