Glute bridges does dick all for squats and deadlifts (nothing because of the short range of motion, and add nothing but strength at that specific range of motion), but hip thrusts are a pretty solid choice as a tier three (accessory) exercise if you have issues pushing your hips through in the squat or deadlift or you just have a weak ass.
Like, you could do your squat, then bust out 3X10 Sumo SLDL's, then 3X15 hip thrusts, 3X10 weighted back extensions, and 4X8 side bends if you have shitty hip strength in your squat.
However if you don't have absolutely shit tier glute strength, I wouldn't recommend them for the deadlift. If your lockout/knee area strength is weak then do some pulls against chains/block pulls after deadlifts or mixed in as a main movement then hit the shit out of your posterior chain with a mixture of back extensions, SLDL's, glute ham raises, and rows then finish off with abs.
So you could one day for example work up to a triple with deadlifts against chains, do three heavy sets of rows or SLDL's then get 50 reps of GHR's, 3-4 sets of heavy back extensions, then something for abs.
edit: I have no idea why I quoted budreiser at this point.