In the 1908 Presidential election
William Jennings Bryan made his third run for the Presidency, and it was his worst running yet. But if he waited 4 years, when the Republicans were split between Taft and Roosevelt, could he first win the nomination, and could he have finally won the Presidency?
No reason at all why not. Some Democratic leaders felt he was a bit "past his sell-by date" but he was still hugely popular with the party's rank and file, and would probably have coasted through the Primaries, esp if Clark decided not to run.
Also, TTL he is quite a bit less shopworn. The Dems will have lost twice with Bryan, but also twice without him, and the latter two defeats will have been heavier than the former. The sentiment to give him another go will be at least as strong as in 1908 and probably stronger.
As for November, there's no reason why he should have any problem. After all, even in 1908, facing the handpicked heir apparent of a hugely popular incumbent, he did better than Wilson would do four years later. In 1912, with the Republicans in a total train wreck, he will surely get at least the 43% he got then, and quite possibly more - maybe around his 1900 score of 45.5%.
The votes may be differently distributed. Bryan could lose one or two New England states that Wilson took OTL, but he'd probably pick up Utah and California, and if he equals his 1908 performance he could even edge TR out in Pennsylvania. Not that it matters. He could lose all NE and gain nothing, and he'd still be around the 400 electoral vote mark.