Historically the strongest wood glues for bowmaking were those with rigid glue lines, like urac and resorcinol. The most stressed point on a wooden bow glue join is at the dip area, and a flexible glue line can break down there, resulting in a lift or even the handle popping off. I only use proven glues on this area eg bowmakers epoxy, urac, resorcinol. Titebond 3 can fail, so can epoxies with a flexible glue line.
Full length laminations , ie back,core, and belly are much safer as the ends of the glue line are only exposed near the tips.
A more flexible glue line can safely work there. Titebond 3, is my glue of choice. It is waterproof, cheap and does an excellent job there. Most decent epoxies will work too.