[The Squatter of Amon Rûdh]

I think that in this case 'bitter' means that their separation was bitter to both of them, not that it created bitterness between them. In the book, Elrond is far more resigned to his daughter's choice, although he does make it a condition of Arwen's marriage that Aragorn should take up his inheritance and reunite Arnor and Gondor.

The point is that the decision is Arwen's to make. Elrond knows better than to make it for her, however painful their parting may be for him. Tolkien repeatedly points out that it's just as difficult to do the right thing as it is to know what the right thing is, and Elrond, Arwen and Aragorn are old and wise enough to do what must be done and endure what must be endured without complaint. I think that certain interpreters have missed that point. The clumsy attempts of film-Elrond to prevent a match of which he had been aware for decades would eventually prove futile and only make his parting from Arwen all the more bitter. Elrond can hardly be expected to be overjoyed at losing his daughter forever, but Tolkien's character has the wisdom and nobility to give in gracefully. Such behaviour goes against the grain of human nature, but I hope that it's still not entirely incomprehensible.