The fumigating bombs only really work in a fairly airtight space so other than finding something safe to spray the bales with I don't know what to suggest - you'd probably have to ask some specialized companies about safety
We have swallows too - they do a great job of eating other bugs so I tolerate them - and its such a delight to watch the young ones grow and eventually learn to fly but once they've gone I spray all around the nesting site and remove the nests - wearing gloves as they're usually crawling with mites
I have automatic fly spray dispensers all around my barn - they might help in yours.
Celeste We are going to stop feeding that hay. Untill it freezes and the bugs will die. I have more hay in another barn I can use.
The mites don't harm the horses none of them have bites or itchy at all.
I won't be spraying the hay .