Well, when you're logged in as root, the bash history is saved in
/root/.bash_history file, where
/root is the default home directory for root user. To prove this, run the following command when you are logged as root:
$HISTFILE variable points to the file that contains your history.
Generally when you log into another user account, the bash history will be saved in a file called
.bash_history located in the home directory of that user.
Furthermore, if you want to save the bash history for the root user in another file, let say in
.bash_history file from my home directory, you have to edit
/root/.bashrc file, and add a new line at the end of file with the following content:
HISTFILE="/home/username/.bash_history" #change username with your user name