To dispose of petri dishes after using them for bacteria you need to kill the bacteria that you grew in the petri dishes.
To kill off bacteria that you grew in the petri dish you take some household bleach and pour some bleach into the petri dish.
The bleach will kill the bacteria that was grown in the petri dish making it safe to dispose of in the trash.
So after you kill the bacteria in the petri dish with bleach then put the petri dish into a bag such as a grocery bag and tie it closed.
Then just dispose of the petri dish into your normal trash but always make sure you kill the bacteria in the petri dish first so that the bacteria doesn't spread.