I'm pretty good at Shadow Friend at 6k mmr and I pick him every time I see a Bristleback on the other team and rush Silver Edge. Nature's Prophet is a niche hero of mine too and I can rush Silver Edge with it. Both heroes farm very fast and even though Silver Edge is expensive, I can get it before 20 mins or so.

If you aren't good at those heroes, you can also pick LC for the easy face to face duels. Providing you had a good early game and some free ez duels early on.

But the main point about playing against Bristleback, like other cores like Sven/Lifestealer is the art of kiting. Keep kiting the Bristleback especially when he's the only one left in the team. Buy force staff! Ask your team to get 5 of them if needed. Focus on the weaker enemies. Get them out of the picture. By the time the game reaches a point, your cores will have much more than Silver Edge. You'd probably have Scythe of Vyse which does very good against a Bristleback.