How to refresh all bash shells using a command/script?

No I don't think this is possible. Nor should it be. This would basically amount to a way to inject code into an already launched and active shell and would pose a significant security threat.

Many daemon processes are designed to do this. The typical way would be to send them the HUP (hangup) signal which causes them to re-launch after re-reading their config files. You could trigger this with something like:

pkill -HUP daemon_name

However when doing this on bash, bash just shuts off. It's not a daemon and the system doesn't have it behave like one.

The long and the short of it is that you probably won't keep making changes to your bashrc so frequently as time goes on and it won't be much of an issue. When you do make changes, you will just have to re-source the file if you need the changes in running shells.

There's nothing built into bash. You could tell it to maybe reload .bashrc each time it displays a prompt, through PROMPT_COMMAND.

## Create a timestamp file, dated like the .bashrc that was read.
## There is a small race condition: if .bashrc is modified as the shell is
## just starting, before getting to this line, this instance won't detect
## that modification.
bashrc_timestamp_file=~/.bashrc-timestamp-$$
touch -r ~/.bashrc "$bashrc_timestamp_file"
## Remove the timestamp file on exit. The timestamp file will be left
## behind on a crash.
trap 'rm "$bashrc_timestamp_file"' EXIT HUP TERM INT QUIT
maybe_reload_bashrc () {
  if [[ ~/.bashrc -nt $bashrc_timestamp_file ]]; then
    . ~/.bashrc
  fi
}
if [[ $PROMPT_COMMAND != *maybe_reload_bashrc* ]]; then
  PROMPT_COMMAND="maybe_reload_bashrc
$PROMPT_COMMAND"
fi

This is a lot of trouble an extra file accesses for what it's worth. Also, it puts a constraint on your .bashrc: the file must be idempotent, i.e. you must be able to load it more than once with no ill effects. For example, in the snippet above, I take care to add maybe_reload_bashrc to PROMPT_COMMAND only if it's not there already.