If you think she's got a weird allele of the barring gene,Question.
Should I breed the Black hen to a solid rooster, or Barred? Was thinking about breeding her to a solid rooster, but not sure it'll show anything.
and if her father looked like he had normal barring,
then whatever she's got would be recessive to barring.
So breed her to a solid rooster, to see if whatever-it-is shows up in her sons.
Whether it's related to barring or not, you could also breed her to her father, breed her parents to each other, and breed each of her parents to a different mate, to try to see what is going on. All of that could take a while, and you will probably get a confusing mix of results unless you really know the genetics of the ones you're breeding them to (and maybe even then!)
Or you could just shrug it off, decide it's weird, and go on to investigate other things instead of trying to follow up on this. I know you tend to have a lot of projects going, and I don't know how much time & effort this one is worth to you.