First of all, it isn't up to Bloomberg to "rebuild" the towers. Second, it was clear shortly after 9-11-2001 that the twin towers were never going to be rebuilt. Too many victim's families objected, on the grounds that the footprints of the towers were now "hallowed" ground. Additionally, many didn't seem to have the guts to rebuild them.
What is being built is a single tower 1776 feet tall, which is well under way at this point (36 stories so far). See the link below for more details.
Thanks for the link to the new World Trade Center. It will be taller than the original twin towers. By what few snippets of information that I see related to Mayor Bloomberg, I got the impression that there was no new WTC, only a Mosque. Maybe sometime in the past he talked about the building to replace the twin towers.
Given that the NY legislature initiated the building of the original twin towers, I would think that the local jurisdiction (e.g. the mayor) would have some role in the building of the original towers and its replacement.
It makes sense not to rebuild the twin towers exactly where they were originally situated. Also there were design flaws that contributed to the collapse; maybe these flaws cannot be remedied so easily, not to mention dealing with the psychological affects of having the same design, only being told that this time it is okay.