If by "badger", you mean "boar", then yes, there are plenty of good options at that price point!
I don't mean to come off as a *****, but that kind of value really doesn't exist on the market unless you're patient and are lucky enough to score a smoking deal. You'd have to probably ~double that to get in the ballpark of a used Simpsons or a Whipped Dog. But, maybe Rudy Vey can swing something....worth a shot!
However, with that budget point, you can easily pick up a high-quality boar brush from Semogue, Omega, or Proraso. Maybe even two!
I honestly love my WSP 2 band Prince/ silvertip ....59 bucks for luxury tip brush is a good deal.Looking for a cheap (under $20) BUT GOOD entry level badger brush for a friend of mine. Ideally i'd love a Super Badger, but I know that's asking alot.
+1 on the BSTUnder $20 for a silver tip is gonna be difficult to swing, but keep your eye out on the BST. Amazing deals do happen. My first badger hair was a tweezerman, and while they get mixed reviews I never really had any issues out of mine. Good luck in your search Sir!
Vintage Blades has a brush for under $40.00.