Every time the terminal size changes, usually bash will resize automatically so that the LINES and COLUMNS are recomputed correctly. But for some reason this isn't working within a Docker container running bash interactively.
I have shopt checkwinsize -s in my bashrc in the Docker container (and verified that it is on using shopt). Same with the host bash session.
I'm out of ideas, really; shopt checkwinsize -s is the only method I have found for getting bash to automatically evaluate resize when the window is resized.