You have to be very careful about rendering pine pitch. It is very volatile and can burst into flame if it gets too hot. It's best to do this outside for safety sake. That said, I use a veg can on my wood stove. I do watch it closely and remove it from the hot surface before it gets too hot. Also, it will give off a heavy pine scent that might be offensive to other inhabitants. Outside it shouldn't matter.
I think a double boiler might not get hot enough to melt the pitch but it might be hot enough to keep it liquid as you are blending the other ingredients.
I've never used a recipe but just add enough bees wax to make the pitch less brittle, maybe 2/1 pitch/beeswax. I use finely ground charcoal and again enough to give the mixture body. That you will have to play with. This is what I use for hafting points and blades. For a bow finish you probably want more wax and/or lard, maybe equal parts of each. It needs to be more of a paste than a glue.
I also make a pitch varnish for waterproofing sinew wraps on arrows. I dissolve the hard pitch in denatured alcohol. A pint size canning jar works well. Just add the pitch and cover it with the alcohol and give it a day or two to dissolve. If you keep the lid on the jar it will keep indefinitely. If it thickens you and always add more alcohol.
