Using heftier diodes (and the bridge), as George suggested, is always a good thing. The problem with rectifiers is that at the peak of the voltage they should stop conducting (being suddenly polarized in opposite direction), but in reality current will rapidly drop to zero and will keep going (diode conducts in opposite direction) for a short moment, then snapping back to zero. This extremely short current spike (triangle) can induce noise in any circuit inductance (any loop). Good diode should be fast, but snap back slowly. They are called "Soft Recovery Diodes" and Hexfred is example of that. Softness of the diode is often measured as the ratio of recovery time after the peak of the spike to time before (two sides of triangle)
https://www.jedec.org/standards-documents/dictionary/terms/reverse-recovery-softness-factor-rrsf
https://www.jedec.org/standards-documents/dictionary/terms/reverse-recovery-softness-factor-rrsf