The difference between "Wir wissen Bescheid." and "Wir wissen." is that the former idiomatic, while the latter is not.
In general, the verb "wissen" is almost exclusively used with an object ("Er weiß es.", "Sie weiß davon", ...) or a descriptive phrase ("Sie wissen, wo es ist.").
The brief statement "Ich weiß.", which is usually uttered to indicate the speaker already knows about a fact, is some kind of an exception. This becomes apparent when we try to turn that sentence around to anything other than first person singular: "Du weißt.", "Sie weiß.", "Wir wissen.", "Ihr wisst.", "Sie wissen." all sound kind of incomplete. Unlike "Ich weiß.", all the other forms make me want to add an "es" at the end, or turn it around to "Das weißt du.", "Das weiß sie." etc.