It would depend on the context. It means anything between "I very much want to be with you" to "I very much want to have sex with you." In the first case, the sentence might be: "whenever I think that you might leave me, I want you so bad(ly)" In the second, "I want you so bad(ly) right now."

"I want you so bad" is normally used with a sexual implication. It will be understood like "I want your body so bad!" Even if it is not meant to be sexual, it will more than likely be comprehended in such a way.