I rub 2 or 3 coats of beef tallow or even hog lard into my bows real good, and then after all that has soaked in as much as its going to, I rub off the excess and then burnish. You don't need to oil as you burnish, the 2 or 3 oats will already be in the wood when you do it and be more than enough. After it is all slick and shiny, I sometimes add a light coating of lindseed oil as a final coating to add more durable protection against moistre.
Beef tallow highly preferred as a burnishing oil, but just rub into the wood before not during.
=Matt