Go to Honor Hold (if you are Alliance... I assume Thrallmar if you are Horde) in Outlands to level your mining past 300. The Blacksmithing trainer there should also have more BS for you to learn at your current level. If I remember correctly I was able to learn the Fel Iron Plate Set right around the level of BS that you currently have, and I was able to learn to mine/smelt Fel Iron at the same time. Fel Iron is ABUNDANT in HFP, so farming for mats for the Fel Iron Set was tremendously easy, and the items only took 4-8 bars of Fel Iron to make (no other mats required) so my BS level went up pretty quickly until these items went green/grey.
Also, some items require that you choose between Armorsmith and Weaponsmith before you can learn them. I believe there are still quest chains associated with becoming an Armorsmith or Weaponsmith, but they are really easy if you are higher than level 40 when you do them and they are well outlined on this site.
Edited, Oct 29th 2008 11:41am by jeromesimina