Looks like you're pretty much stuck if you don't have a vehicle, as I couldn't find any public transit in Sterling at all. If someone knows the area, is this true?
I have a theory, of course I have no facts, so this is just speculation.
Theory - An older guy
Kaitlyn may have met an older guy online and they began talking. Maybe he got her a cell phone that was mentioned in the flyer for them to talk without her parents knowing. Lets assume that he has a car. He may have called her on the evening of May 20 and asked her to hang out with him, maybe go to a club, to dance for example and he would bring her home later that night. She quietly left the house and met him somewhere to be picked up.
Now, I've googled bars/clubs in the Arenas county and most (if not all) seem to close at 12 AM or even earlier (I assume because the county is small and quite rural) and there are not that many of them. This leads me to believe that they went to a neighboring county that is bigger. Some possibilities below:
1. Bay County - a county south of Arenas, the county seat is Bay City, population is about 35 000. About 34 minutes drive (35.8 miles from Sterling) on I-75.
2. Iosco County - a county northeast of Arenas, the county seat is Tawas City, the most populated city is Plainfield Township I believe (population about 4000). About 42 minutes drive (36.6 miles) on M-65.
3. Gladwin County - a county west of Arenas. The county seat is Gladwin which has a population of about 2900 and can be reached via M-61 in about 31 minute (26.6 miles)
4. Ogemaw County - a county northwest of Arenas. The county seat is West Branch, with population of about 2100. Can be reached on I-75 in about 23 minutes (24.2 miles).
IMO Bay county is the best possibility.