Generally you're gonna want to use it over Zen Headbutt as Ice Punch provides solid coverage alongside Hi Jump Kick, but as always it depends on the rest of your team.bullet punch medi, y/n? I just have no idea where on the moveset I want it, losing Ice Punch sucks. Also what nature with BP?
Zen Headbutt is usually the better choice over Bullet Punch but BP is still a nice option if you're using a slower team that's lacking a proper revenge killer, since Fake Out + Bullet Punch does that quite nicely. It's also advisable to use it if you're weak to Mega Diancie.
Jolly is usually preferred since Medicham is in a crowded speed tier and Adamant is outsped by all the base 88+ speed mons who do use a positive speed nature, like Lando-T, Tapu Lele and Kyurem-Black. Adamant can still be used if these are not a threat to your team to boost your priority attacks' damage, but more often than not Jolly is still more useful since HJK and Ice Punch are still gonna be your main means of dealing damage.