Two-parter:
1. How much bleach can go in a garden bed depends a lot on the kind of soil, and I know nothin' about Georgia soil, let alone yours.
2. More bleach could go in the soil if the rains were working right to help leach it through. That's not happening.

"Some" bleach should be ok. If you're using used laundry-water for plants, you might want to bleach the things you most want bleached in a bucket. Then wring them out, and throw them in the washer. Save the bucket of bleach water.... You can use it again in a few days, and nothing much can contaminate it. But the amount of bleach left in the washer-water should be fine for plants and other uses.
Linda S