I always prewash. Black is not one of my most feared colors to use, and I deliberately often use it with batiks so it will just catch any dyes they cast off.
I am most suspicious of dark blues and dark reds running... it was a maroon that completely ruined a quilt.
Color catchers are part of my regular laundry supplies, typically if I'm hesitant about a piece of fabric I run a cup of plain water through the kuerig so it is hot and dunk a corner of my fabric. You will know pretty quickly if enough dye comes off of it to worry about. Other than that though, I run my fabric through with like colors of my regular wash and check the color catcher if it darkens. BTW, I did a test and am perfectly happy with the brand I'm finding at one of my local Dollar Tree stores.
Last year I got a bag of hand dyed fabric from the thrift store that had not been properly set. Since I didn't know what dyes were used, I heat treated it by boiling it with salt/vinegar added and rinsing microwaving for a second heat treat, rinsing again, and finally washing. Was a huge amount of effort but it's stable now. Walmart has a surprisingly good selection of products, both in the basic Rit Dye box display and in their Craft kits section, huge section devoted to tie dye.