many viable options
I would suggest keep it simple at first and experiment as you gain success
acrylic is cheap and easy to obtain,,and a clear finish can be sprayed over that,, or brushed,,
oil does go on a bit smoother,, but has its issues as well,,
there is a learning curve with both
you just have to start and see what works best for you,, professional artist have a preference on what medium they like, and don't agree on what is best,,
of course natural pigments have been used forever and are in context with the bows we make,,,,
you could mix the acrylic with hide glue for a more organic effect,, the options are infinite,,
or once painted,, you can glaze over with hide glue to tone the paint down etc etc etc,,
the last bow I painted with artist oil paint,,it looked nice,, I sprayed a clear finish over the paint and it looks quite nice,, but not muted or toned down like a natural pigment,, good luck on your project, I am sure it will look great,,