Bouchard married the girl when she was 15 and he was 19, when both were living in Florida. They divorced three years later, he told the newspaper.
She killed herself when she was 20, Bouchard said.
Online records list a woman with her name as being buried at a Jacksonville cemetery in 1990. The newspaper chose not to identify the woman.
Bouchard, a gun rights activist who co-owns a septic system servicing business with his wife, did not immediately return a phone call from The Associated Press seeking comment.
Framing the story as "Romeo and Juliet" is wrong and dangerous, said Kristen Schwartz, executive director for the Wyoming Coalition Against Domestic Violence and Sexual Assault.
"Laws exist to protect young people involved in these situations," Schwartz said.
"There's a reason we have laws against sexual abuse of a minor and it's because the brain of a 14-year-old is not developed enough to make mature decisions about sex and sexuality."
Schwartz added: "Any language that would minimise things that are a crime is harmful. It's harmful to survivors and it's harmful to our greater community."
Bouchard and the girl were able to legally marry because Florida at the time allowed marriage at any age with a judge's approval if a pregnancy was involved and a parent consented.
He said he and the girl were under pressure to have an abortion, which they refused. The son, now an adult, has become "almost" estranged from him after making "some wrong choices in his life", Bouchard said.
"A lot of pressure. Pressure to abort a baby. I got to tell you. I wasn't going to do it, and neither was she," Bouchard said.
"And there was pressure to have her banished from their family. Just pressure. Pressure to go hide somewhere. And the only thing I could see as the right thing to do was to get married and take care of him."
Bouchard said the disclosure wouldn't stop him from seeking higher office.
"Bring it on. I'm going to stay in this race," he said. "We're going to continue to raise money because my record stands on its own."
Sexual harm: Where to get help:
• If it's an emergency and you feel that you or someone else is at risk, call 111
• If you've ever experienced sexual assault or abuse and need to talk to someone call the confidential crisis helpline
on: 0800 044 334 or text 4334
• Alternatively contact your local police station
• If you have been abused, remember it's not your fault