I believe that there are a large number of ways to prevent your bash history being recorded e.g. export HISTSIZE=0, how can I prevent users from hiding their bash history?
readonly HISTSIZE in your
Use the Append-Only Attribute
You could use root to modify the attributes of the .bash_history file, but this will cause problems when Bash tries to truncate the file to HISTSIZE or otherwise overwrite the file. For example:
sudo chattr +a ~username/.bash_history
With this flag in place, even root can't delete or truncate the file without first remove the append-only flag.
A user can always do "HISTFILE=/some/innocuous/place" which will leave the default history file intact. Thus append-only on the default file will only prevent users from reducing the file, but it does not force users to save their history to the default.
chattr +a .bash_history, which prevents users from deleting the history file.
Of course, users will still be able to change the HIST... variables, but this will show up in the .bash_history. You will be able to check if they were doing things like using a different HISTFILE to cover their tracks.