While Trump can tout the stock market (which is being artificially inflated by the Fed) and unemployment and job creation (low paying, no benefit, service work mostly) it means little if most Americans are not seeing changes and the great economy is mostly benefiting the wealthy yet again. Also healthcare cost and most employer healthcare deductibles have gone up as of 2020 and that promised replacement to the ACA? Delayed again. < grim picture.
I think any advantage Trump has due to the economy isn't really affected by whether or not his opposition calls himself a socialist. It may give him an advantage, but I think it would really be the same against any Democratic competitor. If people feel like Trump's done them good, it's not like Bloomberg would be more able to convince them to "reverse course" than Sanders would. They'd stick for what they feel has worked for them, period.
Trump also has a pretty significant disadvantage in that he has never polled above 50% in approval ratings. Unlike Dubya, who was bolstered by 9/11, there's nothing that has really given him a massive spike like that at any point (and I hope to God that doesn't happen, lol).
I'd say I'm much more bullish about the prospect of Trump being a 1 term president than I was three months ago. I figured he was almost certain to get re-elected. In part, this was because I thought the Democrats would mount a weak challenger like Joe Biden who would just repeat Hillary's talking points. Now that the likelihood of that has gone down, I'm more optimistic (although I do not see it as inevitable). It is essential to not go into this election letting Trump and Republicans define the terms of the debate; that gives them the advantage, as it usually has in the past.
My first presidential election was against a Republican incumbent president; I've been worried that history would repeat itself, but I think there's a good chance that it won't happen if Sanders gets the nom. I truly believe that Sanders has the best chance against Trump. This is a time of populism; very few people actually were that crazy on the pre-Trump status quo to begin with.