Physically mining nodes is not the only option to power level your mining. For some steps it may be feasible to buy ore off the auction house and smelt it. You can get your mining from 1 to 140 from smelting without ever touching a mine but it will be very expensive because some of the ores are rare, if you wish to skip these first steps and power level your mining to 140 from smelting see the Smelting 1-140 section at the bottom of this guide.
How many hours to power level mining would you guess? I'm thinking about dropping my 275 enchanting for mining, just to make a bunch of gold. I'm level 70, and I have an epic mount for the old world, a normal flyer for outlands. If I focused strictly on mining, smelting all my copper until it won't skillup anymore, any guesses on how long this might take?

Expect it to take you probably 2-3 days to max skill mining. It mostly depends on how easily you can find the nodes you need to level up. The hardest part is typically thorium since it is typically very heavily farmed. Since you are a lvl70 though that should make things a bit easier since you can go places most others can't that are still leveling mining.

Both goldshire, and dun morgh are great places for copper
Deadmine runs and Loch Modan are good for Tin
Darkshire usually gives a health mix of everything from copper on up to iron including gold and silver
Iron is usually best found in arathi with the occassional mithril and truesilver
Mithril is most often found in badlands along with some iron.
Thorium can be found in un'goro, WPL, EPL etc... For you I would probably suggest checking out winterspring

Once you get past thorium the rest is easy, just mine fel iron pretty much all over outlands with helfire probably having the highest concentration of fel iron.

Anyways hope that helps. You can smelt your way up to about 100 mining, after that smelting no longer gives you levels.