I tried fine tip sharpies on a couple bows and disliked the results. I'll never use them again. I used Jelly Roll pens for years with good results, but now use Faber-Castell India ink pens.
I write on the bare wood, though often it's dyed, then spray a misting coat of Thunderbird over the lettering, allow it to dry for 1/2 - 1 hour, then commence spraying.