Unknown source of noise when measuring with oscilloscope
The most likely culprit is your bench supply. First thing to do is look at the regulator input. If you check the data sheet, you'll see that the output noise figure is specified for a bandwidth of 10 Hz to 10 KHz, and the spikes you see on your scope have much higher bandwidth that this. There is no specified response time of the regulator to changes on the input, but it is certain to be much, much slower than those spikes.