My second oldest helped me lift hives into almonds last year and he was 11, but has been helping with the bees since he was 9. My oldest is 13 and wants a paintball gun so i told him if he helps me move them into almonds this year i would help him, and he did! And he doesn't have the slight bit of interest in bees, but after that night, I think he does now!
My youngest is 9 and has been around the bees since he was 6 and likes to help as well. Then my daughter who is 10 likes to do the honey extracting/bottling end of things!
I think when you think your kids are ready to go to the bee yard is completely up to you, just make sure they are protected so they don't get stung and never want to go again!