Why doesn't the force of gravity change the speed of a bowling ball as it rolls along a bowling lane?

Because the gravitational force, which points downward, is perfectly balanced by the normal reaction of the floor of the bowling lane, which points upward. The two forces are equal in magnitude, so the net force acting vertically on the bowling ball is zero, therefore there is no acceleration along this direction. Moreover, since the ball is moving in the horizontal direction, the gravitational force has no component along this direction, so it does not change the velocity of the ball.