Bitter shortbread - what to do with it?

I'm afraid there is not really much you can do. I once wrote up a catch-all question on trying to remove an overpowering smell from food; in your case, what I said applies to the bitter taste too. (The exception for taste are foods where you can leach it out, such as aubergines).

You already hit on the one technique that has a chance of helping: adding something else, both to dilute the unwanted taste and to distract the senses with a competing taste. I am intentionally saying "has a chance of" and not "will" work - the results are very subjective. For some people, a given combination will be sufficient so they will no longer be bothered by the presence of the bitter taste, for others, it will not be sufficient. This variability is also the reason why nobody can suggest a magic combination that will mask it better than others.

To your subquestion, there is also no obvious reason for this to happen, unless you are using "browned" as an euphemism for "almost charred". This is a very standard recipe, and with so few components, the probability of two things reacting in unexpected ways is minimal. You can of course try baking it less next time, or changing the butter, but at this point, it is really a matter of wild guessing.

Based on my experience rescuing overdone oatcakes, I suggest crumbling up the shortbread, maybe cutting off any obviously burnt edges, adding some sugar and then using it as the topping for a fruit crumble. You could add another complex taste by adding crumbled nuts to the topping. (Mix them in, else they will burn during the baking.) There will probably be some bitterness remaining, but I'd expect this to mask it and make something palatable for most people.