Could somebody explain to me what I'm supposed to be doing here? I've been playing it as a bit of a bend, but I'm not convinced that's correct.
Always start the shake figure by holding the first note slightly. For a descending shake you then go up a step, back down to the first note, then to the second note. Notice in your example the second note of each shake has a teepee articulation, so honor that.
On brass the shake is done with the lip.