In his eagerness to secure the bear he took the chance of his single bullet disabling it.

A reckless game it was, but he played it and lost.
Jimmy was unarmed and Bobby had no time to reload, for he knew the bear would charge immediately.
"Run, Jimmy! Run for your life!" he shouted.
But Jimmy needed no warning.

He was already putting into action all the speed he could muster, and away went Bobby, also.
Jimmy chose the open space nearer the shore, Bobby a more direct, though more obstructed, course across the island, but both took the general direction of camp.

As the two diverged the bear, probably because he was more plainly in view, chose to follow Jimmy, and followed him so strenuously and with such singleness of purpose that he was presently at Jimmy's very heels--so close at his heels, indeed, that had Jimmy stopped or hesitated or lessened his speed for an instant, the infuriated beast would have been upon him.
Bobby was quick to discover that the bear had left his own trail, and he was also quick to discover Jimmy's imminent danger.

There was no other help at hand.