A bridge rectifier is 4 diodes. Test them as such. A diode conducts in one direction and not in the other.
Any simple continuity tester or mutli meter can be used.
Usually when diodes fail they start to conduct in both directions and you know its bad because it blows fuses, trips the breaker etc supplying it.
Take a multi-Meter and switch it to Ohm x 1
Test between one of the "~" and "+" legs.
You should get either an almost-zero reading in one direction, and when you reverse the test probes, you should get an almost infinite ("sleeping 8") reading.
Now try the same between this "~" leg and "-".
Same as above.
Now repeat the same tests with the other "~" leg, and "+", and then "-".
Same as above.
If you either get almost zero or almost infinite in BOTH directions, then the rectifier is fried.