How to put a support bed under an already installed bathtub?
I have done this with plain Plaster of Paris, which I consider to be the best option - it's stable, but easily removed if/when the tub is replaced. I had planned to set the tub, pull it and place a pile of plaster, then reset it, but setting it the first time was such a chore that I did it from the other side of the wall instead. 

It will be a bit messy, so prepare for that. With plaster you need to keep the relatively short working time in mind (it sets fairly quickly) and be sure to push enough in from the side you can access to support the opposite side. I ended up mixing several smaller batches so that I could get them placed before the plaster set, and filled in from the far side to the side I had access from with successive batches.