Bear
Encountering a bear triggers immediate, primal terror. The human brain contains ancient circuitry specifically designed to recognise and flee from large predators. A charging grizzly produces adrenaline responses that can be measured in nearby observers. Bear safety courses exist because the fear is rational - these animals can and do kill humans. The phrase "bear attack" requires no explanation in any language. This is fear with teeth, claws, and a documented body count.
Time
Time inspires a different, more insidious fear - existential dread. The awareness that time is passing, that youth fades, that loved ones age, that death approaches with mathematical certainty - this fear underpins entire philosophical traditions and keeps therapists employed. Humans have invented religions largely to cope with time's implications. We fear the bear for what it might do; we fear time for what it will certainly do. The bear might kill you. Time definitely will.
VERDICT
The bear wins in immediate, visceral terror. Time wins in sustained, inescapable dread. One can avoid bears by staying out of forests. One cannot avoid time by any means yet discovered.