I think that st does not have a menu bar. What are you referring to? Perhaps you mean the title bar [1]? If you are referring to the title bar or any other window decoration [2], they are drawn by the window manager, so you need to tell the window manager to display full screen. What window manager are you using?
On the other hand, Firefox's View > Full Screen (F11 key) does seem to do the trick, regardless of the window manager. If it were possible to get st to do the same thing, such a feature would probably not be included in the main repository due to the preference for small fast and simple that characterizes suckless programs. But it might be accepted as a patch [3]. [1] https://upload.wikimedia.org/wikipedia/commons/1/14/Window_%28windowing_system%29.svg [2] https://en.wikipedia.org/wiki/Window_decoration [3] http://st.suckless.org/patches/