Hunter weapons, bows for example, don’t get to have any enchant effect (animation).
However, I’ve found one bow that has an enchant animation. The bow’s name is Avalanche and it can be farmed in Ulduar.
The enchant is the PVP 2.2k enchant from arena season 13. It looks pretty awesome, a red-dark glow that leaves some sort of shadows when you move your character.
The thing is that I tried to transmog my s13 pvp weapon with all the bows from my bank and none are showing the enchant effect. And I have almost all the bows from the game. All except Avalanche, I’m not sure why.