A bridge can crack because of stress, lack of humidity, a defect in the wood, or a combination of any of them. Typically it cracks thru the bridge pins, although it can crack thru the saddle slot. Or it can crack anywhere along its length due to a weakness in the grain.
The saddle slot crack is probably fatal and the bridge will need to be replaced. These cracks usually are thru the whole length of the bridge. If the bridge is broken into 2 pieces, epoxy might work as long as you keep the gap between the pieces to a minimum.
However, a crack thru the bridge pins or in the grain can be repaired. The first step is to humidify the bridge to bring the 2 parts back together. Never just fill a crack with glue and assume it will be OK. The repair would be ugly and probably won’t hold.
WARNING: This will be initially very ugly. If not done correctly glue can run onto the top of the guitar, damaging the finish. After the bridge is glued the whole top of the bridge will need to be sanded to have a consistent finish.
Water thin super glue, only available at hobby stores. It will wick deep down into the crack and soak into the grain, but is not meant for gap filling. Do not use regular super glue, it will just sit on the surface.
2” wide painter’s tape.
Sheet plastic or newspaper to protect the top of the guitar in case glue is dropped on in.
Heavy sheet plastic to make a sanding guard around the bridge.
Be sure there isn’t any debris in the crack that will keep it from coming back together.
Cut a piece of sponge to fit over the top of the bridge.
Thoroughly saturate the sponge and squeeze out most of the water.
Place the sponge over the center of the crack.
Place a small weight on the sponge to force the sponge to contact the contour of the cracked area.
Depending on the ambient humidity (you aren’t keeping your guitars in under 40% humidity, are you??) rewet the sponge once or twice per day.
Repeat until the crack is closed or no more progress is made for 1 day.
Remove the sponge and let the area dry for 1 day.
Cut a hole in the heavy sheet plastic to fit around the bridge, and lay in on the top of the guitar to protect it when sanding the bridge.
Press a piece of masking tape onto the bottom of the bridge plate to keep any glue from dripping into the guitar.
Cut a rectangular hole in a piece of painters tape to fit around the crack. The area must be covered with one continuous piece of tape without gaps. Do not overlap layers of tape, the glue will find its way thru the corner and onto the finish.
Tightly tape your plastic or paper on top of the first layer of tape, pressing very tightly in the corners of the overlaps.
Tape another layer of plastic or paper on top of the first, keeping the tape overlaps away from each other. The glue will find the finest crack and follow it. The second layer will keep it from finding the top of the guitar.
Carefully squirt the water thin super glue into the crack, doing your best to keep it from running onto the tape. The glue is actually thinner than water and runs quickly.
Let it harden for a few minutes, then check if there are any small voids in the crack. If so apply more glue.
Once it looks like the voids are filled, remove all the plastic and tape.
Allow the glue to harden until the surface isn’t tacky and sand the area smooth, with the sanding guard in place. Some wood dust will be pushed into the glue, further hiding it.
If there are any voids repeat the previous steps, add more glue and sand again.
Fine sand the bridge (up to 600 grit) to smooth the area glued, and to even out the color. Be sure all scratches have been removed or the finish will highlight them.
Apply oil or finish if required. I use Howard Feed-N-Wax.