Congrats on the new friction machine.
My first comment is to keep it as simple as possible. I think the BOGO stuff is too hard. Here's what I seen, and what I plan to do with my new conveyor in the future.
1. For a week offer it as free. You might be tempted to do this for a day, but the power of this is the word of mouth that can get their friends to tell their friends and make it there in time to get a free wash too. You can have a sign there that says "tell your friends on Facebook" (and have a Facebook page if you do this). Also, try to get free PR from radio, newspaper or other civic groups in the area.
2. For a week (or a second week if you do free), then offer washes at 50% off. All day long, all night long. Again, for a week. You'll still get buzz, and get the people who finally got around to getting their "free" wash their friends told them about. You won't get PR like #1. This might work best for you because you have a touchless right next to it, and it might be ignored with #1 -- not sure of the economics of how much it would take for a touchfree customer to put their car in brushes. Interesting science experiment!
3. Do facebook with a twist, not just a regular ad. Here's what I do for an existing wash, but works anytime -- every fall, spring, winter, summer I give away 13 washes to a lucky person. All they have to do is enter to submit a comment and like the page. Coupled with a boosted (aka paid) post, you will go viral. I am in a town of 3500, and get 1600 views about my contest and 400 entries every time. Use a facebook random contest winner website (google it) and pick a winner. I like this option least for a new wash because it doesn't get the experience. It gets people to know you have a new wash, but doesn't get people to try it.
Anyway, I'd do all 3 if you can afford it. We have a lot of luck with Facebook, but I wouldn't pay $200 on Facebook, tho to boost a single post. Give away value (the car washes are cheaper than the Facebook ad rates) and you'll get the same effect. You just need to ask people to share with their facebook friends. The #3 contest will get by with $50 of boosts tops, less if you have an established Facebook page (you don't). I pay about $20 to boost this post, myself.
Also, I used this promotion to get to about 1300 likes in a town of 3500. I give away $3 off coupons on this site too, so people subscribe for that.
BOGO good idea, but too complicated. Especially if your preppers are busy. Plus they'll pay full price to experience your wash the first time, which means your hurdle is still there. Getting them to give you a like at the car wash is probably too complicated too. You can ask, and hopefully they do it in the bay while fiddling with their phone during the wash, but it's not likely.
PS. When you set up your free business facebook page, make sure you stock it with likes before you do much with it. The best way is to ask all your personal friends.
Good luck!