I have the same issue. I was wondering if you grow your own beets then I think you could use water with some H2O2 (Hydrogen-Peroxid) and Iodine drops to spray the plants and I am sure the bugs would not eat them. I found good fresh leaves only once from a supermarket, but I thought they must have used some fertilizer to keep them that way. My last purchase was from a farmers market and he took the greens back so that he can feed his animals.
I would not eat the ones with the bug bites. I would love to hear from others.