I believe, there is no such thing as "bubble down". But, you can use Bind.ModelWithoutContext to move action target to your child ViewModel:
<Button cal:Message.Attach="DoIt" cal:Bind.ModelWithoutContext="{Binding Path=ChildViewModel}" Content="Test It!"/>
There is "some" documentation on https://caliburnmicro.codeplex.com/wikipage?title=All%20About%20Actions. Hope it will help you.