I think it is crazy to have your bunny hill merge into the bottom of intermediate/expert trails. No matter how many "SLOW" signs you put up, people are going to come in hot.
Either dedicate a hill/lift entirely for ski school, or only have other beginner runs merging with the bunny hill at the bottom. But yeah, it is scary for little 5-year-olds when some 17-year-old buzzes them at 40mph.
I wonder if the little girl had a helmet on?