Bristlenose are fantastic at pooing, so I would say no to one in a tank that small. I personally would say no to a group of badis too, more on the grounds of they prefer live foods, and knowing how piggish betta can be, I can see one out competing any badis. Badis can also be quite territorial from what I've read, which is why they do better in a longer tank- there's more room for different territories and more room to add plants and bogwood, etc. to break the line of sight. Just because a fish is small doesn't mean it will do well in a small tank
If you're worried about the betta eating any cherry shrimp, why not go for a smaller group of ammano shrimp? They're fantastic little creatures and are really fascinating to watch!