Forrest achieved fame when bandleader Artie Shaw hired her in 1938. Shaw was looking for new talent when vocalist Billie Holiday had to leave the band after singing with the group for a short period of time. Forrest recorded 38 singles with Shaw's band. Two of her biggest hits with Shaw were the songs "They Say" and "All the Things You Are."

In late 1939, Forrest left Shaw and joined Benny Goodman, with whom she recorded a number of celebrated songs, including the hit song, "The Man I Love." She told the Pop Chronicles "Benny would look right above your eyebrows, in the middle, right on top of the brow. He was a very strange man."

She recorded with Nat King Cole and Lionel Hampton in 1940. In 1941, Forrest was hired by Harry James. It was with the Harry James Orchestra that she recorded what are arguably her most popular numbers, including "I Had the Craziest Dream" and "I Don't Want to Walk Without You." Forrest also dated James, until he met the woman he would later marry, Betty Grable.

Because of her involvement with most of the popular bands of the big band era, Forrest was known as "the voice of the name bands."

Forrest left Harry James in late 1943 in pursuit of a solo career. In the late 1940s, she sang on Dick Haymes' radio show. It was with Haymes that she recorded the song, "Some Sunday Morning."

In 1944 she made an appearance in the Esther Williams movie Bathing Beauty with Harry James and his orchestra. After a dip in recording in the 1950s, Forrest sang with Tommy Dorsey's orchestra, led by Sam Donahue in the early 1960s. She continued to sing in supper clubs in the 1970s and 1980s. Her final album was released in 1983.

She kept singing until the early 1990s, when arthritis forced her into retirement. Over the course of her career, she recorded more than 500 songs. Forrest also acted in several musical films, including Bathing Beauty and Two Girls and a Sailor, which both came out in 1944. She was a civil rights activist as well.