That definitely looks strange. If one of the diodes in the rectifier failed open, you'd have a half wave rectifier. Which clearly isn't what you have on the scope. Now if one of diodes is shorted, you are going to draw a massive amount of current. But you said you got the above waveform by applying voltage across the BR with an isolation transformer. Does your isolation transformer have a fuse (most do)? If it does, it would have likely blown if one of the diodes was shorted in this rectifier. If we use the photo below as an example, the positive going side of the AC sinewave being rectified by D1 and D4 would not be affected, but the negative side would. You'd effectively be shorting the secondary winding of the transformer. So either the transformer would eventually fail open or diode D3 would fail open due to the overcurrent.