These stages were supposed to refer to having a terminal illness, not about the death of an important person. As with many things, popular media has misrepresented them so much that even some professionals and halfway professionals have gotten things mixed up (call it "the psychopaths and the bumblebees" effect, if you might)... And even that popular misconception aside, the research was slightly doctored to be more supportive of the hypothesis.

That said, you can experience some form of all of these when losing a loved one. Maybe not all, maybe not in this order, and probably also some that are not mentioned in that list. (Incidentally, I would also differentiate shock from denial and sadness from depression.) If your loved one was ill/injured before death, you may start grieving before they are gone, which can give the process a somewhat greater resemblance to coming to terms with your own impending death (although the final outcome of bereavement will likely be going back and forth between sadness and acceptance, rather than firmly staying as acceptance; the sadness becomes less intense over time, but will still be there). For example, after a reasonably expected death that was not someone's fault, a person might only experience numbness(shock), emptiness and sadness, in roughly this order...

In general, the more unexpected the death, the stronger and more prolonged the shock/disbelief at their passing will be. Basically, people feel numb, surreal, shocked at first and (except for cases of pre-emptive grieving) the actual sadness may follow hour or days, sometimes weeks later. (Sidenote: in extreme cases, shock may yield anything from screaming and scrambling to see the dead person to just shutting down for an extended period of time.) The general feeling of emptiness and, if formerly seeing frequently/living together, the acute awareness of the interruption to your life in the person's absence causes are common for both unexpected and expected death. https://www.ncbi.nlm.nih.gov/books/NBK217845/

Anger is one which is most dependent on manner of death. Bargaining is probably the least likely to be expressed (since unlike when living with terminal illness, the subject is already dead). Some people can feel relieved at death if the loved one was suffering. Guilt is very common, but not even mentioned in the terminal illness grief list. ("What if I had done something differently?" - could be anything from convincing them to not go base jumping to seeing them more often during their last year of life. These being examples of self-blame and regret respectively. Here is one article dealing with the connections between guilt and bereavement in a bit more elaborate fashion - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4018291/ ).