Born in Queens, New York to parents Luke and Susan Betos, Michelle began playing soccer at age five. She attended St. Francis Preparatory School in the New York City borough of Queens. She was a two-year captain on the soccer team and was named 2005 Most Valuable Player. She played for the Albertson Fury ’87 from 2004–2006 and was a member of the Region I Olympic Development Program team in 2006. In 2005, she was named an ENYSSA State Team player and participated in the Super Y-League Olympic Development Program National Camp.
Betos attended the University of Georgia. She finished her college career with a total of 316 saves, ranking third all-time at Georgia and second in shutout count and win totals. During her senior year, she started all 22 games, logging 1,929 minutes and earned eight shutouts and a goals-against average of 1.12 per game. Her junior year, she appeared in all 23 games making 22 starts. She recorded seven shutouts and a 1.19 GAA, finishing the season with 117 saves. Betos was named SEC All-Tournament Team and SEC Defensive Player of the Week on October 21, 2008. In 2007, she started all 24 games, finishing with 18 wins, eight shutouts and a 0.79 GAA. She recorded a save percentage of.816, making 84 saves and allowing 19 goals. She was named the team's Defensive Most Valuable Player. During her freshman year, Betos appeared in 12 games in goal, making eight starts. She led Georgia in GAA, save percentage, fewest goals allowed, wins, shutouts and saves. She was named to the SEC All-Freshman Team the same year.
Betos played for the Atlanta Silverbacks of the W-League during the 2009 season. She was named W-League Goalkeeper of the Year after leading the Atlanta Silverbacks to the regular season Southeast Division title. She finished the season with a 9–1–1 record and the team finished 10–1–1. She ranked second in the league for her 0.188 goals-against average, nine wins and nine shutouts.
Betos signed with Apollon Limassol in the UEFA Women's Champions League for the 2012–2013 season. She recorded five appearances for the team for a total of 450 minutes.
In the 2013–14 offseason, Seattle traded Betos and Kristie Mewis to the Boston Breakers for Sydney Leroux. Boston soon traded Betos to Portland for the thirty-fourth pick in the 2014 NWSL College Draft. Initially serving as a backup to Nadine Angerer, Betos made 14 starts during the 2015 season. On June 19, 2015, Betos scored the equalizing goal for 10-man Portland in the 95th minute against FC Kansas City. This was the first ever goal scored by a goalkeeper in the NWSL. Her goal was featured on ESPN SportsCenter as the #2 play during the show's Top 10 feature. She was subsequently named NWSL Player of the Week. Following the season, she was named NWSL Goalkeeper of the Year. Betos was part of the 2016 Thorns team that won the NWSL Shield.