I don’t think TR runs if Bryan is the dem nominee so Taft wins
First of all, the Democratic convention was held after the Republican one, so it was already clear that TR would be running as a third party candidate. Second, there is no reason to think that TR would change his mind because the Democrats nominated Bryan. In OTL, some supporters urged TR not to run once the Democrats had nominated Wilson (whose nomination was rightly or wrongly seen as a "progressive" victory against the "conservative" Clark). No, TR replied--even if Wilson was himself a progressive, as the Democratic candidate he would be dependent on big city machines and the Solid South, and could therefore not be an effective progressive president. He would probably say the same thing about Bryan. Besides, TR was in favor of regulating the trusts rather than breaking them up--and in that sense was in fundamental disagreement with Bryan and Brandeis and La Follette. "The fact is that many of the men who have called themselves Progressives, and who certainly believe that they are Progressives, represent in reality in this matter not progress at all but a kind of sincere rural toryism. These men believe that it is possible by strengthening the Anti-Trust Law to restore business to the competitive conditions of the middle of the last century. Any such effort is foredoomed to end in failure, and, if successful, would be mischievous to the last degree.."
https://books.google.com/books?id=P101DwAAQBAJ&pg=PT417
