Bryne grew up in Leixlip, County Kildare, and attended secondary school at Coláiste Chiaráin. Already a promising goalkeeper, she played for St Patrick's Athletic in the Dublin Women's Soccer League and then agreed to join professional Danish Elitedivisionen club Fortuna Hjørring after completing her schooling. After spending one year in Denmark, Bryne returned to Ireland because she was homesick and took a job as a secretary with the Health Board.
When Arsenal Ladies' goalkeeper Lesley Higgs was injured, the club's Irish midfielder Ciara Grant alerted Arsenal manager Vic Akers to her friend Bryne's availability. Byrne joined Arsenal in January 2000 and quickly became their first choice goalkeeper. She won a domestic treble in her first full season with Arsenal, saving a penalty in the 2001 FA Women's Cup final win over Fulham, and was voted club Players' Player of the Year in 2003 and 2005.
She became a European champion with Arsenal in April 2007, when they beat Umeå IK in the 2007 UEFA Women's Cup Final 1–0 on aggregate, a tie in which she made numerous vital saves in the home and away games. In 2008 she rejected an offer to join American Women's Professional Soccer franchise Boston Breakers, who failed to match her salary expectations.
Byrne was given a free transfer by Arsenal in December 2016 on the expiry of her contract, after being supplanted in the team by Sari van Veenendaal. She agreed to join FA WSL 2 club Brighton & Hove Albion Women for the FA WSL Spring Series. On 4 August 2017, 38-year-old Byrne announced her retirement from football on Twitter.
Byrne made her first appearance for the Republic of Ireland women's national football team on 31 March 1996 against Belgium. She won her 100th cap against Croatia on 26 September 2013. Following the retirement of Ciara Grant, coach Sue Ronan named Byrne the team captain in March 2013. In April 2017 a player revolt led by Byrne secured substantially improved working conditions for Ireland's female national team players.
Byrne previously worked in the Football Association of Ireland (FAI) ticket office and was later employed as a coach in Arsenal's academy. She married former professional footballer Marcus Bignot in June 2013.UEFA Women's Champions League: 1
FA WSL: 2
FA Women's Premier League National Division: 9
2000–01, 2001–02, 2003–04, 2004–05, 2005–06, 2006–07, 2007–08, 2008–09, 2009–10
FA Women's Cup: 9
2000–01, 2003–04, 2005–06, 2006–07, 2007–08, 2008–09, 2010–11, 2012–13, 2013–14, 2015–16
FA WSL Cup: 3
2011, 2012, 2013, 2015
FA Women's Premier League Cup: 5
1999–00, 2000–01, 2004–05, 2006–07, 2007–08