However, if you insist on running around on your mount (I hope it's epic, for your sake) power leveling herbalism you can start in any of the 1-10 zones. Run around Durotar until you're level 75 and then visit the nearest large city for an herbalism trainer. Keep in mind you can use this trainer all the way through Artisan Herbalism. You won't need to learn Master Herbalism until level 300 and you can find a trainer in Thrallmar or Honor Hold.
If you're power leveling Herbalism and you have your epic mount head back to The Barrens and keep collecting until you're level 150. Stay in the northern Barrens until ~110, then head south. If you're on a PvP server and you're alliance you will be better off going to Silverpine Forest for this.
Next you're going to want to head towards Arathi Highlands where you will stay until level 225. On your way head to the Wetlands and get at least 20 levels so that you can collect Fadeleaf and Goldthorn when you get to Arathi Highlands
Once you're level 225 head to Feralas where you'll stay until 275. Stay south during the lower levels (the first few will be slow, then you'll be able to pick Sungrass and this'll become one of the quickest 50 levels)
At 275 it's time to head to Western and Eastern Plaguelands. These 25 levels will come very quickly especially if you have an epic mount. Start at Chillwind Camp and run towards Light Hope's Chapel. If you're not 300 by the time you get there do a few loops around the scars and you'll be set. Feel free to stick around the plaguelands until level 325 (although you'll need to learn Master Herbalism from Honor Hold or Thrallmar anyways), this way you can avoid the competition and potential PvP in the Outlands.
Leveling to 375 is really easy and there are no routes to grind or areas to farm. If there is a specific herb you want to collect you can focus on it. For example: Netherbloom is only found in Netherstorm and is used to make Super Healing Potions (used to level Alchemy). Although I wouldn't recommend heading to Netherstorm to pick herbs without a flying mount. Alternatively, you may consider farming Aldor or Scryer rep and consequently finding many herbs doing it.