Do sulfate reducing bacteria ingest their sulfate as solid, or as dissolved in water?
Sulfates in water would not be liquid. Their melting points are far to high. When a sulfate dissolves into sulfate ions and some cation such as potassium, we say it is solvated, not liquid. Sulfates would also not be present as gasses due to their ionic nature as well as high molecular weights. So that leaves solvated sulfate ions and solid sulfates that have not completely dissolved.

To be ingested in bulk as a solid would require endocytosis which is not performed by prokaryotes: http://faculty.ccbcmd.edu/courses/bio141/lecguide/unit1/proeu/proeu.html

Further research indicates sulfate, as ions, enters the cell through permeases: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.532.943&amp;rep=rep1&amp;type=pdf

Edit: Here's some files to help with the idea of how ions and other molecules enter cells. Again, bacteria do not engulf substances whole, in the process of endocytosis, such as eukaryotes are capable of. Here is an image of a nitrate ion within a transport protein. Only a few amino acids of the protein are shown here, the actual protein is much larger and spans across the entire membrane creating a channel for the ion to enter. http://www.rcsb.org/pdb/ngl/ngl.do?pdbid=4U4W&amp;preset=ligandInteraction&amp;sele=[NO3] 

Here's another channel, aquaporin, which allows transport of water across the membrane. http://pdb101.rcsb.org/motm/173 The top left image shows the channel in the protein leading to the interior. The third image down shows the interaction between the water and the amino acids (backbones only are shown) which facilitate the water's passage.