Alena Bienz was born on 5th March 2003 in Wolhusen in Switzerland, 20 kilometres from Luzern. At the age of six, she began to play football at FC Entlebuch before joining FC Luzern in 2015. She also featured for SC Kriens for a season in 2018-19. Afterwards, she spent the next three seasons with FC Luzern in the Women's Super League and won the 2021 Swiss Cup. In her final season in Switzerland, Bienz scored seven goals in 12 games and scored twice in three play-offs games.
1. FC Köln signed Alena Bienz at the start of the 2022-23 season and secured the services of one of Switzerland's most promising attacking talents. In the last 16 of the DFB-Pokal in her first season, Bienz scored a last-minute equaliser against Turbine Potsdam to help her side progress to the next round.
In February 2023, Bienz was nominated to the Swiss national team for the very first time and headed to Spain for two games against Poland.