/etc/bashrc is the system setting. The usual place to change the prompt would be the per-user file, ~/.bashrc. You might already have a setting there that's overwriting the system default. Put your prompt string in ~/.bashrc.
Furthermore, there is a quirk in bash's handling of initialization files. The /etc/bashrc and ~/.bashrc files are only read for interactive instances of bash that are not login shell. If you run a login shell, bash only reads /etc/profile, and ~/.bash_profile (or ~/.profile if it doesn't exist). You need to explicitly source your .bashrc from your .bash_profile if the login shell is interactive:
# Work around a well-known bash design bug: bash does not read .bashrc if
# it is invoked as a login shell.
case "$-" in *i*) if test -r ~/.bashrc; then . ~/.bashrc; fi;; esac