TB3 usually dries in 24 hours but like JW said some of the moisture in the glue will migrate into the wood. There will still be some moisture from the sinew also.Maybe scraping the birch bark from the belly will speed up the drying some.
I think we may have lit on your problem. Some of the moisture migrates direct to the atmosphere from the back of the bow and some migrates INTO THE WOOD! Think about how long it takes to get the last moisture seasoned out of a piece of wood. And especially if you have a finish over the belly of the wood to help block the migration of that moisture! There is a reason why those old bowmakers building sinew composite bows took their sweet time. Dry to the touch and cured are two completely different critters.
I am going to counsel putting that bow up somewhere out of the way but where air regularly circulates. It's not a head of lettuce that's wilt on ya, or an eg that's gonna go off. Think of it as a fine wine that needs to mature and come into its own. I'm gonna say give it six months.
I think I like that course of "action"! I'll give it some months to really cure. I'd hate to scrape the belly since the strips I used to cover the belly are overlapping the sides and cover the seams from the back layer. It was a long day of prepping all the bark and another one to glue it on. The limbs are both twisted too so depending on how you look at the bow it either looks fine or slightly uneven. At least it's the lower limb that's stiff for now!
Thanks so much for the input, much appreciated!