I hate that everyone can only analyze politics as a pundit, so I'll give my personal view of Bloomberg before I discuss his chances:
My time in NYC almost completely overlaps with his time as mayor. I did not vote for him the first time around, because I was so sick of hearing the whole "We just need to run government like a business" schtick, but I was forced to admit that he proved to be a much better manager than I expected (and also much better than most CEOs-turned-politicians). He really did hire good people, and in the wake of Rudy, who saw dramatic reductions in crime while also inflaming racial tensions, it was nice to see someone prove that you could have the former without the latter (for the most part; more on that in a second). I also liked that he thought big -- even if the West Side stadium and 2020 Olympic bids may not have been the best ideas, I liked that he had a long-term vision. In the meantime, he implemented a number of small quality-of-life measures that made living in the city more enjoyable, like increased bike lanes, larger pedestrian areas around Times Square and elsewhere, and Citibike.
The negative: I really hated his move to abolish term limits in order to give himself a third term, then immediately supporting a referendum to reimpose them after he had won. That was such a big issue for me that, after voting to re-elect him in '05, I refused to do it again in '09 (although I viewed his opponent as a hack and only voted for him because I assumed he had no chance of winning; as it turned out, a lot of people felt the same way I did and Bloomberg nearly lost). Also, while he was a million times better than Rudy on race relations, he was strangely pig-headed about continuing stop-and-frisk. Similarly, the fact that he was so close to Wall Street bothered me a little, but his stubborn refusal to see how things had changed after '08 bothered me much more, and belied his pragmatic image.
As for how all of this would translate to the White House, I'm a little skeptical. The NYC Mayor is an incredibly powerful role, one that suited Bloomberg's personality (and Rudy's too, for that matter). Being president requires a lot more consensus building, and I'm not sure I ever really saw that in him (then again, I was wrong about him the first time, so who knows?) He is also a little too moderate for my taste, particularly on economic issues. But he's an interesting voice to add to the mix, and I hope he runs.
All that said, putting my pundit hat back on, he has zero chance of winning the Democratic nomination. Think of it this way: the energy driving the Democratic base right now mostly comes from four groups: young people, women, African Americans and Sanders/Warren economic populists. The first group would have no particular reason to love him (especially given his age). The second two would at best, view him with a healthy dose of skepticism (I already discussed stop-and-frisk, but check out his recent
tone-deaf comments on #MeToo). And the last group absolutely hates him. I also think the media tends to overstate the chances of tri-state area politicians as well as the popularity of socially liberal/fiscally conservative views (if anything, it's the opposite that is more popular, which Trump cleverly tapped into.)