With the amount of money at stake, I would say, it is definitely worth doing. It's a bit like cutting your own hair -- it might be more of a learning experience than an outright victory at first, but it has a *huge* lifetime earnings potential.
I have both lived with roommates and rented rooms in other people's houses. I am an introvert as well. A couple thoughts:
1 - Quite possible you can find someone who works a schedule very different from yours. For example, maybe you'll find someone who works a 3-11 shift. That'll mean that the roommate (possibly) can hear you when you get ready for work in the morning, but falls right back asleep, and you (possibly) can hear your roommate when s/he comes home at night but you fall right back asleep as well. But it's mostly like alternating who lives in the apartment.
2 - Think in advance of whether any particular food smells are going to drive you bananas. Probably my worst feature (as a renter of a room in someone else's house) is that I microwave semi-smelly vegetables, like broccoli, cauliflower, Brussels sprouts, carrots. Nothing a little fresh air can't cure, but still something that might be annoying.
Offer something that has a natural ending. "I'm renting out a room in my house till the end of May" is going to be something that can't really go very wrong.
Once you are able to get your extra room rented, then even if there is a day where you are both at home all day, it wouldn't be out of the question for you to go blow $8 bucks reading your book at the Starbucks instead of on the couch. Still a net savings of $492, right?
Incidentally, be clear that you are just renting out the room, not renting out half your house. In other words, common areas are yours and access to the laundry room and the kitchen is only fine with the understanding that the person leaves it as they found it. Your renter can't bring others into your house when s/he wants to hang out with friends.
Keep the rent amount in proportion to what you are actually renting out (should be somewhat cheaper than people looking for a roommate, who would share all bills, chores and common areas), and you might find yourself with a good mustachian roommate.