I think the irradiation produces elctron-hole pairs in the semiconductor, which can react with adsorbed water or oxygen on the surface to reactive species like O2- or .OH, .O, O-, O3-...

As explained nicely by Nico Lämmerhardt . Generation of ROS( reactive oxygen species are the main reason for ZnO anitbacterial activity. Other reason such as dissolution of Zn ion also play a critical role in Antibacterial activity. ROS retard the generation of ATP  by mitochondria and also affect badly DNA replication processes and these all lead to the apoptosis thus cell death. 

Have look on this paper.

There some differences in antibacterial activity under UV or visible light. Concerning visible light,  both defects (and correspoding localized electronic states at band gap) and ROS (depending  on the system OH or O-realted ones) are important. This is an open field of research. Some studies comparing UV and visible light or the effects of radicals (in TiO2) could help you to analyze the situation:

https://www.researchgate.net/publication/237836001_UV_and_visible_light_optimization_of_anatase_TiO2_antimicrobial_properties_Surface_deposition_of_metal_and_oxide_%28Cu_Zn_Ag%29_species

https://www.researchgate.net/publication/260253085_Understanding_the_antimicrobial_mechanism_of_TiO2-based_nanocomposite_films_in_a_pathogenic_bacterium

Article UV and visible light optimization of anatase TiO2 antimicrob...

Article Understanding the antimicrobial mechanism of TiO2-based nano...

Another reason for antibacterial activity of these nanoparticles has been reported which relies on the reaction of these salts in the aqueous medium to release metal Ions and these metals can substitute themselves with for example Fe-S bonds in bio-molecule's structure to cause their malfunction and programmed death.