Silver is a rare spawn of a node that is normally a Tin vein. So, while you can find Silver in any area that has Tin, there is no guarantee that any of the Tin has spawned as silver.
You need to pretty much concentrate on the regular ores and hope for the random rares like Silver, Gold and Truesilver.
Remember that you get skill-ups off of mining an ore long after it goes gray to you for smelting.
If you are looking for Tin (and hoping for Silver), any 10-20 zone like the Barrens and Silverpine will be good. Since you are level 46, you might be better off in a zone like Ashenvale, Stonetalon, Hillsbrad, Thousand Needles and Arathi where you should find Iron as well as the Tin and Copper.
After Iron comes Mithril and the zones you are currently questing in should have a decent amount of Mithril scattered around. I seem to remember a frustratingly large gap to level up skill in before I could grab those Truesilver veins that were constantly taunting me.