I'm about to finish a pink bow and arrow set for my niece as a graduation gift. I didn't use RIT on this one, somebody gave me the dye. I have used RIT on other bows. Just keep adding more dye powder until it gets to the right shade that you want. Like Macbow said, test it on some scraps until you get it right.
Here are a couple pics of the bow and arrows I'm working on. The bow is backed with solid black snake skins. I have a pink and black string to go with it. Sorry for the low quality cell phone pics.
The feathers were dyed with RIT mixed with water. This was my first try at skinning arrows.