If I would play a bounty hunter, I would go either for teeth, bones, fur or feather, unless my bounty hunter have some taxidermist skills. Any flesh will start to rote after a while, so unless you are a troglodyte, you don't want that. Also, the larger the item, the else you can carry without being overburden. No glory to have only a few trophy, unless they are quality.
But at the same time, you could have a bag of holding that preserve you trophy. But doing that, you would probably become worst than any girl with her handpurse.
The guy take his handbag: "Sorry, my signet ring is somewhere in that... found it, it is stuck between the teeth of my dragon head... ouch! My finger! Damned Troll head, always regenerate after a while..."