Unfortunately you can't purchase a Rune Pickaxe like you do in OSRS. The easiest way to obtain one would be to complete Clue scrolls. Otherwise you'd have to kill General Graardor, Venenatis, Callisto, Vet'ion, or Cerberus for one. But by the time you'd have the stats to kill those bosses you may as well go for the Dragon pickaxe, easiest and safest boss to obtain one would be from KBD.
Pickaxes bronze-rune have the same speed (they are equal) so useless if there was a numorf pickaxe shop.
Dragon however is better and can be obtained through bossing.
This was correct until last update. Pickaxes/hatchets have been updated to be faster/slower dependant on their tier/required level of use as it is on OSRS.