To automatically set widow title in GNU screen you can use PROMPT_COMMAND environment variable like it suggested here or here. Content of PROMPT_COMMAND will be executed by Bash before displaying command prompt.

On my gentoo default bashrc (/etc/bash/bashrc) already contains PROMPT_COMMAND rules, though for some reason they were not working correctly in my case.

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case ${TERM} in
        xterm*|rxvt*|Eterm|aterm|kterm|gnome*|interix)
                PROMPT_COMMAND='echo -ne "\033]0;${USER}@${HOSTNAME%%.*}:${PWD/$HOME/~}\007"'
                ;;
        screen)
                PROMPT_COMMAND='echo -ne "\033_${USER}@${HOSTNAME%%.*}:${PWD/$HOME/~}\033\\"'
                ;;
esac

Another way of automatically setting screen title is by embedding special escape sequence into command shell prompt. The simplest way I found for achiving it is placing

PS1='\[\033k\033\\\]'$PS1

to the end of ~/.bashrc file.

Your screen’s shelltitle configuration parameter should be configured correctly according to your command prompt. For example if your prompt ends with $ than shelltitle could be “$ |bash”.