I never attack bears and wolves, as they're too dangerous. I catch them in traps and pelt them with rocks until they die (which leaves the skin in a good shape). With wolves I have occasionally gone in to melee range to get some dodge training (and retreat as soon as an injury is sustained), but I wouldn't do that with a bear.
(Lost my last character to a wolf in an Injured Adventurer quest: The wolf attacked, thrown javelin missed, spear thrust missed, dodge missed, bit in arm, unconscious, dead. All the skill checks were down to an effective level of 75 due to injury and encumbrance, from 90).
I don't know if death to starvation in a trap is counted as you killing a bear, but I doubt it. Likewise, I doubt a bear would be weakened by starvation, but if it was, you could try to leave it in a trap for a number of days and then try your unarmed probably suicidal attack.