How will Colored Bows work?

Yes, bows will function like dragonstones when it comes to inheritance! You can see it if you search for a skill on the inheritance tab.

Personally, I really hope coloured daggers become a thing. I've been saying for a while (long before coloured bows were implemented) that I think the best fix to daggers would be to give them colours. Idk if they'll make them a thing, though, since it'll just inflate the coloured pools unless they're going to restrict coloured bows/colourless dragons to legendary heroes.