Any substance that produces ions is a good conductor of electricity... since base produces ions in water they are good conductors of electricity(strong bases)....for example sodium hydrooxide pottasium hydroxid etc. however weak base are not good conductor of electricity same is for acids...

experiment to prove strong bases conduct electricity :

1. take a beaker full of water, dip two wires in it..
2. connect the wires to a bulb and a battery..
3.without addition of base the bulb doesnt glow which means that electricity is not passing..
4. add a strong base and bulb starts to glow, it means base allows us to conduct electricity i.e. they form ions in water to carry electric current...