Realistically, an Independent run by Bernie would effect the election minimally. Sure, he would get more votes than he did OTL, but for the most part, the Dems would come back to their party, and the GOP would do the same.
A couple of close states (Minnesota, New Hampshire, At-large Maine) would probably swing to Trump, but is seems unlikely his (Bernie's) campaign would gain enough traction to do anything more than that.
However, even without Bernie getting that much traction, the Hillary's margin in NYC, New York, and other huge cities would drop, possibly delivering the popular vote to Trump, but even that is unlikely.
Bernie did have a rather large following, so it is possible for the Democratic vote to be completely split. Bernie had strong appeal among young liberal voters, while Hillary had appeal to moderate Democrats.
I don't think Bernie would take big states like California or New York, but I could definitely see him take his home state of Vermont and maybe Hawaii (if he is very lucky).
