Greenway joined Drake in 2022 after five seasons as the head coach of Grand View University.
During her tenure as a Bulldogs, Greenway has helped lead Drake to another historic season in 2022-23 as the team took down No. 22 ranked Nebraska 80-62 early in the season and eventually captured their seventh MVC Tournament championship and their 14th NCAA Tournament berth in program history. The Bulldogs traveled to Austin, Texas for the NCAA Tournament where they battled No. 5 seed Louisville to the last possession. Greenway then helped guide the Bulldogs to the program's 10th MVC Regular Season championship in 2023-24. It was the eighth MVC Tournament championship and second in a row for Drake, who visited Manhattan, Kan. for their second straight NCAA Tournament berth.
In her time at Grand View, she led them to three NAIA National Tournament appearances, coached the 2021 Heart of America Player of the Year, and held a 97-60 record. She also spent three seasons as an assistant coach at Grand View prior to becoming head coach.Prior to her stint with the Vikings, she spent six seasons with North Iowa Area Community College – three years as an assistant coach and three years as head coach. During her time with the Trojans, she led them to the Regular Season and Tournament Champions in 2014 when they were ranked No. 1 for 11 out of 13 weeks.
She earned her bachelor's degree from Iowa in 2008 where she spent three years as a Manager for the Hawkeye women's basketball program. She also holds an associate degree from NIACC where she was a member of the basketball team for two years. She earned the 2005 Female Student-Athlete of the Year.