A bye has to count as a full win. A player should not be eliminated from the running for first place (in a tournament with no cut especially) because they were randomly chosen to get the bye. You just can't penalize a player for something they had zero ability to control.
Agree with ScottieATF. 4 points for the bye. It's enough of a downside that it will contribute 0 points to your Strength of Schedule, it doesn't need to have points cut too.