I've read that some bacteria can survive a long time without food. What constitutes the death of a bacteria ? What process needs to take place for it to be considered dead?
When you talk about organisms like fungi and bacteria which can have a dormant form, and viruses, "dead" becomes somewhat harder to define. In fact, it has not been definitively defined for bacteria.
I would have guessed "when they are permanently unable to reproduce", but I may be wrong.
From one source:
The observed coordinated gene expression continued even after cell death, in other words after all bacteria permanently lost their ability to reproduce. Transcription of a very limited number of genes correlated with cell viability under the applied killing regime. The transcripts of the expressed genes in living bacteria – but silent in dead bacteria-include those of essential genes encoding chaperones of the protein folding machinery and can serve as molecular biomarkers for bacterial cell viability.
it is a challenge to determine if bacterial cells are dead, or viable but non-culturable (VBNC), and what is an agreed upon correct definition of dead bacteria.
Some viable but nonculturable cells (VBNC) can be "resuscitated" into dividing cells. 
However, the simple binary definition live/dead probably does not accurately describe the complex physiological states possible with microbial cells.
Unfortunately the actual conclusion is behind a paywall.
Finally, another country heard from5 :
Programmed cell death is a gene-directed process involved in the development and homeostasis of multicellular organisms. The most common mode of programmed cell death is apoptosis, which is characterized by a stereotypical set of biochemical and morphological hallmarks. Here we report that Escherichia coli also exhibit characteristic markers of apoptosis—including phosphatidylserine exposure, chromosome condensation, and DNA fragmentation—when faced with cell death-triggering stress, namely bactericidal antibiotic treatment.
So, perhaps the answer is, a bacterium is dead when it is unable to reproduce, cannot be resuscitated, gene expression has ceased, and shows characteristic markers of apoptosis
 Transcriptional activity around bacterial cell death reveals molecular biomarkers for cell viability, Remco Kort, Bart J Keijser, Martien PM Caspers, Frank H Schuren and Roy Montijn, BMC Genomics 2008
 Can dead bacterial cells be defined and are genes expressed after cell death? Trevors JT1, J Microbiol Methods. 2012 Jul
 A matter of bacterial life and death Gregg Bogosian, Edward V Bourneuf
Advances in microbial food safety: 23.
 Antibiotic-Induced Bacterial Cell Death Exhibits Physiological and Biochemical Hallmarks of Apoptosis, Daniel J. Dwyer, Diogo M. Camacho1, Michael A. Kohanski, Jarred M. Callura1, James J. Collins, Molecular Cell, Volume 46, Issue 5, 8 June 2012, Pages 561–572