Bassler was the President of the CERN Council from 2019 to 2021,[1] and deputy director of National Institute of Nuclear and Particle Physics (IN2P3), CNRS, from 2014 to 2015.

[3] She joined the Nuclear and High Energy Laboratory (LPNHE), a joint research unit between the Centre national de la recherche scientifique (CNRS) and Pierre and Marie Curie University, where she worked on collider-based particle physics.

[4] Bassler used data from the HERA particle accelerator, where she worked on the structure of the proton as a member of the H1 experiment at DESY in Germany.

[7][8] She was part of a working group on structure function providing input to the Deep Inelastic Scattering Workshop in 1999.

[4] At IN2P3, Bassler prepared the approval of the upgrades for the high-luminosity LHC (HL-LHC) detectors and the French participation in the European Open Science Cloud.