It is possible and easy to selectively remove entries from your bash history (say, for commands involving a password), using the following commands:
history | grep <stuff I am looking for> history -d <corresponding number> history -w
If you want to delete the whole history:
history -c history -w
The ‘w’ flag is necessary to write the changes to the history file (~/.bash_history) as this is done asynchronously.
Full details at Raw Syntax.