To start with, FDR and Bloomberg were/are members of the Democratic Party. Mostly right wing Republicans call it the Democrat Party, as an affront.
FDR famously said that he was not a socialist. When he sensed the end of his life was near, he dumped Progressive, Henry Wallace, from his ticket and brought in Traditional liberal Harry S Truman as VP. The reason almost all of the programs of the Emergency Relief Appropriations Act of 1935 required people to work for money, is that FDR did not like the "dole," (what we call welfare) and paying able bodied people who did not work. His "Social Security Insurance," program was designed to protect workers from being destitute when they were old, and no longer able to work. It is easy to surmise that a man who believed people should work for what they get (FDR) would not support all of the "free," programs Sanders proposes.
As the Myers-Briggs program points out, a person as far to the left as is Sanders will see almost everyone else as being to the right. One of the things that Bloomberg proposes is to fix the problems created by Reagan that underpays large numbers of people on Social Security who worked and paid in for decades. Many of these are school teachers, whose retirement programs do not pay into Social Security. Reagan used that as an excuse to reduce their benefits for work they did that was covered by Social Security. Why didn't Bernie fix this, his many years in the House and Senate? I guess taking care of working people is not high on his list of "revolutionary" ideas.
Medicare wasn't even a consideration for FDR. The germ of the idea was introduced by Truman, who Henry Wallace ran against, after quitting the Democratic Party. So much for so-called progressives being loyal.
If FDR lived in these times, he would be worth many tens of millions of dollars and would have the types of investments Sanders condmened in Hillary Clinton. There is no reason to think that Sanders would hide his disdain for the very rich FDR. And, FDR would have little regard for the socialist, Sanders. Don't try to re-write history. If necessary, I will go back and refresh my memory. Sanders is not, and has never been a New Deal type of Democrat. Bloomberg comes a hell of a lot closer to being like FDR, than does Bernie, no matter how much you dislike him.