That realy sucks Tal! I had the same thing happen on the LAST house i rented. It was on a slab and the clog was out by the cespool. I don't think the main pipe had a big enough slant to it and, of course, the tub was the closest fixture to the drain.
Don't bother cleaning it out till the problem is fixed, then run hot water shower a little at a time untill all the crap is out, then clean, clean, clean! That water goes to the same place as the toilet so no need to try and move it out of the tub into the toilet.....Just let it drain.

- Slow -