Krazy (Crazy) glue or other superglues may not be the best to use. I did some research on this when my son's Epiphone guitar popped the bridge, and found out it's not really such a big deal to do. While the Ep had a lifetime warranty, the shop owner noted that sending it in to them, with the long wait, may not be worth the trouble for a simple repair.
Glues that don't soften with heat are not recommended because the wood can be damaged if you ever need to remove the bridge. Super glues and Gorilla Glue are not recommended for that reason. Hide glues are great but you have to mix them up if you can find them locally, but good old Titebond original wood glue works really well, and it can be found in most hardware stores. It's best to remove the old glue completely if possible, not by sanding (sanding tears the wood fiber and weakens the joint, I learned from my old aircraft A&P license exam days).
Ironically, glues that soften with heat can get hot enough locked up in a closed car in the sun to soften them, but at least if that should happen, it should come of cleanly instead of with splinters of the wood.