At what point....

should I start feeding my bp small rats? He's eating adult mice now.

How big is he right now? That would help us answer it better, lol. Usually people go by the width of the widest part of the bp. If the widest part of him is large enough to fit a small rat, then I'm sure it'd be fine to try one. I'm not good with the mouse and rat sizes yet so I suppose you're asking because an adult mouse is around the same size as a small rat? I guess if it looks like your snake can fit it in the widest part, go for it.

He's about 24 inches long.

Yeah, like I said, my advice would be: if the widest part of his body is large enough to fit a small rat in there, try it.
Although, I'm not exactly the expert you should listen to or anything, lol. I haven't even got my bp yet(10 more days and maybe...), but that's just going by what I've learned by doing research and talking to friends who are owners of bp's themselves.

My bp is about 25 inches long and I have him eating rat pups. I ordered them frozen, and some of them are bigger than others. So I'm feeding him all the smaller ones first, he gets them down no problem. I accidently fed him one that was a little bigger once, and it was a little scary to see him stretch his jaw like that, but he still got that one down no problem.

my guy ate rat pups at about a year old or so now he's on weaned and is about a year and a half. Once you switch to rats you will see amazing growth. As long as the prey item is no bigger than their largest part of their body plus about 15% you should be fine. (some say largest part plus 25% but that seems big to me)