What's confusing about it? 
but by the time I went empty my inventory I came back (about 3 minutes)... the damn bear's body was gone
This can be change on the server.properties file.
settings_deadnpc_despawntime=
When I came back (2 minutes later) my body was NO WHERE to be found
These can be change on the server.properties file too.
settings_deadplayers_despawntime=
I suspect the settings are default so low, because they stop low spec machines getting bogged down. If your server/machine can handle it, whack these numbers right up!
The integers represent seconds.
So,
settings_deadplayers_despawntime=900
settings_deadnpc_despawntime=900
Would give you 15 minutes until they despawn.