Answer
The first friend is correct.
Work Step by Step
Let the system consist of both balls.
Suppose the golf ball heads to the right initially, with positive momentum of +1 unit. After the collision, the golf ball rebounds to the left at almost the same speed. Because of its negative velocity, it will have a negative momentum of about -1 unit.
System momentum is conserved, so afterward, the bowling ball must have a positive momentum of +2 units so that the final momentum is 2 + (-1) = 1 unit, as before.
Note that the bowling ball will not be moving very quickly because its mass allows it to have 2 units of momentum while moving much more slowly than a golf ball.
