I think that's a good way of putting it.

Elizabeth is ashamed of how she characterized Darcy, now that she knows the truth, and it's even harder to discuss this with Jane, since Jane knows how much Elizabeth verbally abused Darcy.

But I agree with Kathi above that Elizabeth isn't telling Jane not to mention it because she's afraid Jane will bring it up. Jane isn't the type to bring up unpleasantness of any kind, IMO. In a way, though, it makes Elizabeth's shame even worse, because she has such a forgiving sister, whose opinion she truly values, and she doesn't want to think that Jane is remembering her bad judgement.