Dying on Bleach HD is rather complicated in regards to the system in place to make it so losing your character isn't, well, losing your character- at least not the effort you put into them. Dying is commonplace in the Bleach universe, considering two thirds of the main three races (Human, Hollow and Shinigami) require you to have died in the first place. Not to mention the constant strifing between every race, specifically against the Hollows, you're likely to wound up hurt or worse sooner or later. Death is free reign; if you're out in a topic and common sense dictates another person (or demon as it may be) could join you, they're able to kill you or you them should it come to that. Player killing is not encouraged but it is possible and the system here is in place so that it doesn't ruin you too badly.
Should you die from any cause: whether you be killing off your character out of boredom or for plot, or natural causes take over, or you never quite removed that blade the Arrancar stabbed through your heart, you are able to Reincarnate.
Reincarnation means you can either
A) take this character that just died and move them to the next race on the cycle, retaining the Rank it was at and transferring abilities to their equivalents (kido, base hollow skills and ginto notwithstanding) within the other race if applicable or
B) create a new character, getting a complete experience refund for what you've spent and gained on the character to customize the new one however you'd like.
(With how lenient these rules are, consistently killing off your character when you get bored instead of recreating a new one will not be allowed and will be viewed on a case-by-case basis.)
The Cycle of Reincarnation is a bit wonky and cannot be chosen as an option more than once; it can also not be done for Arrancar or Visored due to them being nonfactors.
If you die as a Fullbringer Human, you can be reincarnated as a Shinigami or Hollow.
If you die as a Quincy Human, you can be reincarnated as a Shinigami.
If you die as a Shinigami, you can be reincarnated as a Human. If you die as a Shinigami due to trying to become a Visored you instead reincarnate as a Hollow, as the Inner Hollow takes over what remains of your being.
If you die as a Hollow, you can be reincarnated as a Shinigami. Should you die at the hands of a Quincy, however, you are forced to take option B or start over from scratch altogether; owning to the fact that Quincy vaporize the Hollow that they kill.
Keep in mind that while reincarnation lets you keep the general appearance, personality and power theme of your character you do not retain your memories. Period.
Happy hunting!