I’m assuming it’s mostly by a combination of dissolving their cell membranes and pulling moisture out of them.

As someone else mentioned bacteria (unlike animal cells) do have protective cell walls made of a substance called peptidoglycan as well, and it varies how thick these walls are and whether they’re outside or inside the cell membrane (which leads to differences in how bacteria take in alcohol-based dye solutions and stain on microscope plates), so that also plays a role in how vulnerable different bacteria are to organic solvents like alcohol.