I think Freudian psychological ideas still have a lot of hold on people, even though in general his theories are generally not taken seriously these days. Under Freud, your emotions are almost like physical substances: you can have “too much” of them, and need to release them. “Releasing” your anger literally removes it from your body in Freudian psychology. I believe this (incorrectly) makes a lot of intuitive sense to people, as it is difficult to maintain a state of full-fledged rage and yelling. ie, you will calm down and the emotion will pass. This is more akin to a biological state: you cannot maintain any feeling indefinitely. But, I do not believe that this means that someone is releasing the emotion in the Freudian sense of the word. In practice, if you “release” your anger in this way often you are simply practicing feeling angry. In other words, you are training your mind to focus on this emotional state, and are therefore most likely increasing the amount of anger you have. You cannot “vent” all this anger because it is not a discrete substance that you can run out of. Instead, you’re behaviorally training yourself to experience anger more often: the opposite what was intended.
To the extent that people can “keep emotions bottled up inside,” I believe this simply means just not addressing a point of contention which makes you angry. The point is not to “release” the anger, but to address this issue which is causing the anger. If you’re not addressing it (either by preventing it or coming to peace with it) then you will keep experiencing the point of contention. In that narrow and non-Freudian sense, you are keeping your anger “bottled up.” But, you cannot just “release” your anger: you must address it. Really, there is no releasing anger; there is merely expressing it.