Nothing like raising your own pests. I have used insecticidal soap on spider mites with success (bought at Lowes). But if they are in your straw, you might just keep raising a new crop of the little nasties.
I use a horticultural oil on ornamentals, but it's rated for vegetable plants also.
It works by smothering the pests.... I suppose you could treat your bales also?
@thistlebloom what's the name of the oil? My plants are coming up and my tomatoes are in danger of getting killed off. Is there an organic method or a specific predator I can attract?
The one I use is called Organocide. I get it at Home Depot. It has an OMRI rating.
If you are over run with them a predatory insect will help, but not eradicate them.