As it turns out, the wool fabric you can see next to the bucket refuses to compost. The cotton and linen I put in the garden in April or May, by comparison, already tears easily; the muslin shreds with a caress of the finger; but this wool does not tear even after many months longer. Perhaps I should shred it and expose it to the elements rather than bury it in compost.
Anyway, I added the old compost along the drip lines of the bushes. The spider pictured spun a web above the compost and lately leaves enough space for me to shove the little compost bucket in there without ruining the web. Every time, I also stir the cover material around so the mites or aphids or whatever will fly up and stick.