I bought one of these a year ago and it seems to do a pretty good job: https://grillbadger.com/

The bristles are a lot bigger than steel bristles, so if one did come off it would presumably be easier to notice in your food and likely less damaging than the stainless steel needles that come off of metal bristle brushes.

This one looks interesting as well: https://www.konabbqstore.com/products/safe-clean-grill-brush...

I also really like this idea: http://www.instructables.com/id/Quick-Bamboo-Skewer-BBQ-Brus...

But you would probably have to wear an oven mitt if you wanted to clean a really hot grill