Bloomberg would have no future. He would never has the 15% consistently to be in the debate. And worse the time at which he would have seriously decided to run would be too late to get into the ballot in some states. He would have given up.
Bloomberg has no campaign, no infra, no DNC or RNC to build a ground game. He would be doing way worse than Nader. I don't think he would be doing even 0.5%. He may take some votes from the RNC but Democrats would back Sanders considering Social Issues & the Supreme Court as Bloomberg certainly is a spoiler
Recall that Bloomberg dropped his pseudo-candidacy in early March, after it became obvious that Clinton was going to win the nomination (apologies to the voters of Michigan). In a world where Sanders wins the nomination, he would have had to have done better on March 1, and in that world Bloomberg would have had well over two months to get onto the ballot even in the earliest states.
He also would have been willing to spend well over a billion in liquid assets on the campaign (unlike a certain other candidate, who neither has that much nor would be willing to spend it, instead hijacking the RNC to do so). That sort of money buys you a campaign, buys you ads, buys you media attention.
Whether it would have taken off is another question...his natural base (well-educated white voters) may not be enough to build a successful campaign off of. At the very least, I feel he'd do at least as well as Anderson '80, however.