Tung oil? As in Tru-oil, or something else?
I'm no bow finish expert but I've used lots of Tru-oil and lots of pure Tung oil (2 different animals), but it sounds like you have too much finish and it hasn't dried hard.
Personally, I would not apply any other finish over either Tru-oil or pure tung oil, but if I had to it would be at least 6-months after, to give the oil time to fully cure.