This is Totally Do-able
My wife and I are stuck in a part of the country with few D&Ders. We do the 1 Dm, 1 PC game all the time. It is fun, emphasizes roleplaying, and allows for a lot more indepth plots, imho.
My advice would be to talk to the player about the limitations of the game. If you both understand it's a different game than a multi-player game is, you'll both be happy.
Tips:
1) Make sure the challange rating for any encounter is viable for your PC. Know their combat abilities and be prepared to scale the game to fit them. Usually an NPC out of the DMG of equal level is a decent encounter. For Monsters look for a challange rating around 2 less than the PC's level. Multiple lower level monsters also work well.
2) Make sure that your PC has a bit better equipment than the average character his/her level. I don't mean pass out the vorpal swords, but healing potions are pretty important to those who don't have healing magic.
3) It's not a good thing to limit the PC's choices, but be smart about your classes. Rangers, Rogues, and Fighters are a lot more viable solo than say a wizard, or bard may be. Although a solo wizard or bard game can be very interesting, they just need extra tweeking and perhaps some henchmen, or NPC party members.
The biggest thing about 1 on 1 d&d is that mentally it's a lot different, more about quest type story lines, more about mysteries, and less about hack and slash. Most modules can't be scaled down for one PC, so you have to be creative, but there are a LOT of resources out there on the
www.
For example, I was the PC of one of our single player games. I was a rogue. I arrive in a town and the city officials hire me to explore an abandoned asylum that they wanted to knock down. I go explore, meet some NPC ghosts to talk to, I figure out the mystery, and I get trapped in a "mental health test" that the old head master set up to torture his patients with. I had to face down a lot of riddles and traps, and deal with the undead head master once I got through his maze.
All that in leather armor with 6 hit points. It was a lot of fun.
I hope this helps, have fun.