There are dyes like tetrazolium that are used to stain activated sludge samples purple indicating that the cells are metabolising, but sure if there are techniques that can be applied to tissues. There could be other staining techniques though?
There are viability assays that use the ATPase activity. These are generally used to find microbial contamination of surfaces for hygiene studies or QA. Again not sure they are applicable in other living tissues?
If you have a suspected bacterium in mind, you can also use immunoassays to test the presence of the antigen (or antibody) in blood/urine/body fluid, etc..
you can detect active bacteria infection by ELISA to detect bacterial antigens or host's immune respose (IgM) antibodies, also you can use PCR or qPCR to detect Bacterial Nucleic acid which is more accurate methods.