It requires a pretty high level of skill/play and Druids have poo for burst so every kill generally takes a great deal of time compared to other PvP classes like your Mages, Rogues, and Warriors. You have to use almost your entire kit to win and basically you have to play at a far higher level than other classes do to secure kills.
Additionally, to garner the best effect Druids that are looking to score kills in solo PvP generally need to run an absolutely ridiculous build that combines Resto, Feral, and Balance.
I recommend checking out some of the Vanilla Druid PvP videos by Sp0h. The following video is the one I remember watching. As an added bonus, the editing is pretty darn good.
https://www.youtube.com/watch?v=byF32oDiEYc