The only way that ANYONE could win as a independent would be for the Republican and Democratic parties to nominate complete joke candidates who party members with any sense at all wouldn't vote for. This country is generally far too polarized for an Independent to win a national election.
The point. A John Anderson might get 40% of the vote if the Democrat is George McGovern and the Republican is Barry Goldwater. One of the two nominees typically isn't so crazy as the other.
Jeb Bush would split the conservative-leaning vote to the benefit of Hillary Clinton. She would win a 44-36-20 split of states that no Democrat has won since Jimmy Carter won them in 1976.
Without such a split I see Hillary Clinton doing well enough to win:
You could exchange Ohio for Virginia.
Because of the involvement of Donald Trump in businesses contrary to Mormon behavior, I could imagine Utah being divided nearly into equal thirds... but basically Bush would split the white vote in the South, with a result like this:
,
yellow representing states that Hillary Clinton wins with less than 45% of the vote