Your bash history is stored on your computer, so there isn't really a difference toward privacy unless you permit anyone sit on your computer. Furthermore, for

Your bash history is stored on your computer, so there isn't really a difference toward privacy unless you permit anyone sit on your computer. Furthermore, for many people, using the command line is part of their daily job. Not keeping a history and/or log, is akin to compiling your source code, keeping the binary and deleting the source. If there are certain things you don't want in your bash history, use the ignorespace capability and explicitly do not store them.