I too live in the country, but on a dirt road. I taught my daughter to ride by holding the seat and running along side her. When I felt she had good balance I let go, but kept running along side. After a few seconds I pointed out that I wasn't holding the bike and that it was all her. She felt safe because I was right next to her. She knew how to operate the brake and I reminded her to do so now- getting winded you know. She stopped and had a grin from ear to ear! She took off on her own after that. Yes, she did wreck a few times, but with her safety gear on she was okay. Again this was on a dirt road and no traffic.
I taught my brothers to ride the same way when I was about 8 years old myself. Works like a charm!
Good luck,
Yvonne