Yep, recovery noise is well known. In this case it might even just be common mode picked up from your wiring, and the diodes being on or off (but not the switching or conduction itself) is simply gating that from your probe.
You actually won't observe any recovery, because 1N4148 is very fast. 1N400x series are very slow (a few us), and will make troublesome RFI even at line frequencies. This is audible using an AM/SW radio and, for the antenna, an inductive loop probe held near the rectifier in most equipment.
The act of a diode going from low impedance to high impedance excites resonances around it, particularly Cj versus wiring inductance. If the inductance is known (or can be estimated), then the ideal solution is to use an R+C in parallel with each diode, where C >= 2.5*Cjo, and R = sqrt(L/Cjo). Often, C >> Cjo is used (e.g., 10nF), which has the effect of dropping sqrt(L/Cjo) so that the resonance, though still present, is just too much of a "thud" to care about.
Tim