How much do they charge to go through the CBX bridge for both sides?

Before entering. The best thing you can do is check online or call them.

30 dls to come and go

They charge 20 dlls or its equivalent in Mexican pesos

To use it you must show your boarding pass that you are arriving by plane to Tijuana, buy your CBX pass that costs you 600 pesos round trip and for the return you must also show your boarding pass that you are already going by plane from Tijuana and obvious your valid passport and visa