Carpenter's glue works fine...I use Titebond to glue on my bridges. As for clamping, I use a system designed and built by Me. It consists of a piece of MDF (3/4" shelving board) cut to approx. 2"X7" with the contour of the bridge cut into the bottom side and three (3) #8 X 2-1/4" bolts with nuts and washers, and a thin piece of wood that will fit between braces at the bridge position. Drill holes thru the both wood pieces that correspond with the (2) outer bridge pins and one of the center bridge pins. Put your glue on the bottom of the bridge. Set bridge in place and put all three bolts (with a washer on each one) thru the clamp, bridge, soundboard and thin inside support piece. Put a washer and nut on the inside of the body. Tighten until you get a nice even glue squeezeout around the bridge and let it dry at least 24 hours with the clamp in place.
I have used this method several times and have never had a bridge failure (yet!!)
If this needs to go to another forum, sorry. I was trying to answer the question and it turned a bridge clamp tutorial.