Picking up Skinning late was a nightmare, imho. Picking up Mining at 70 is actually quite worse.
My 70 Draenei Enhance Shammy is my gold farmer. I got his Herbalism from 1 to 375 in 2 days with no problems at all, albeit tedious, and I make a ton of money off him. I picked up Mining at 70 as well but it's been about 4 or 5 days and still haven't hit 375.
I've spent more time in Silithus farming Thorium than I spent there pre-BC when level 60 was the cap. I won't complain TOO much since stacks of Thorium bars sell for 20g+ and the dense stone is a nice bonus. At the end of it all, I'll have every gathering profession maxed to 375.
Here are a few things to make grinding gathering professions less of a pain in the arse.
Think of the money - Thats right. We all take gathering professions for 1 of 2 reasons. To further your crafting profession or to rake in the gold. If you need motivation to grind your profession, check the AH and see the possible money to be made. You can mine 3 Rich Thorium Veins in 20 minutes and make 60g on my server. Thats faster than doing dailies and shouldn't come with a repair bill.
Pace yourself with music - I have playlists made up of MP3's that lasts about 2 hours. When the playlist is over, I stop farming and take a break. Music will make your mind wander while you're skinning corpses of dead turtles (awwww) or plucking Terocone from Mother Outland. Before you know it, the playlist is over and "BAM!" you have some skillups. I try to aim for more Industrial or ambeint music instead of the normal fast paced Metal-ish stuff. It's much easier for me to farm listening to Skinny Puppy than, say, Slayer. Pick.. Pick.. Pick.. is always a better routine than ZOMGPICKHEBRZRAHHHHHHHHHHH!!!
Set goals - Trying to get from 1 to 375 overnight is only going to burn you out. Some people would rather get it all over with at once instead of pacing themselves but i'm not one to do so. Start off trying to get from 1-100 and take a break. Come back to hit 175, then 275 and up to 375. When I got herbalism up in 2 days, the last thing I wanted to do when I maxed it out was to go farming the next day. Setting up smaller grinding times will make it easier for you to want to farm when you finally max out your profession.
Don't be afraid to be lazy - Thats right. Be lazy if you want. It's your money paying for the game, after all. This is impossible with Herbalism but easier with Skinning and much easier with Mining. I had bored friends with 70's come lay waste to zones so I could skin the dead in a fraction of the time. With mining, pay attention to what level you need to smelt certain ore. The instant you learn to smelt, check the AH (if you can afford it) and buy the ore isntead of going out to farm it. Go back and smelt for the skillups and sell the bars back on the AH for a similar price to break even.
This is all I can come up with at work but if anything else pops up I'll be sure to add them to the post. Enjoy the grind, if at all possible!