Wasser, who has played with everyone from the Scissor Sisters to Lou Reed, began playing violin at age eight while attending grade school in Norwalk, Connecticut. At Boston University, she studied violin with Yuri Mazurkevich and also played with the Boston University Symphony Orchestra, and expanded her horizons to rock with local acts including Hot Trix (which featured Autoclave member and Helium founder Mary Timony) and the Dambuilders, which went on to national success. Wasser also played with Timony and Shudder to Think's Nathan Larson in Mind Science of the Mind, which released their self-titled album in 1996. The following year, the Dambuilders disbanded and Wasser's boyfriend, Jeff Buckley, accidentally drowned in Memphis, Tennessee. Wasser kept on making music, collaborating with the Grifters' Dave Shouse and Buckley's former guitarist Michael Tighe in Those Bastard Souls in the late '90s, and then with Tighe in Black Beetle, which folded in the early 2000s.

Along with working as a violinist for hire with artists as diverse as Sheryl Crow, Hal Willner, Rufus Wainwright, and Antony and the Johnsons, Wasser developed her own songwriting, and formed Joan as Police Woman in 2002. The band released its first single, My Gurl, early in 2003, and self-released the Joan as Police Woman EP in 2004. Joan as Police Woman signed to the British label Reveal, which issued their full-length debut, Real Life, in summer 2006, along with the Eternal Flame, Christobel, and The Ride singles. Real Life was released in the U.S. in summer 2007. To Survive, which featured a cameo by Rufus Wainwright, followed in 2008. For 2011's The Deep Field, Wasser reteamed with Bryce Goggin, co-producer of Real Life, and took a happier, more upbeat approach.