Bucky's been training with Natasha, and, while he'll definitely be on board with saving people, he'll try to get as much information about what is actually going on as he can. So it's possible that he'll have the data for the three of them to decide on whether to try to assassinate the president?

I think if there are signs that the willful stubbornness of the President could be affected by Malicant (because, after all he's seen for the last many, many months, Bucky wouldn't even be surprised by that option), he'll definitely suggest - and try to carry out - elimination of the threat.