If Davis resigned (which his Clintonesque ego would never allow), Bustamante does not "become Governor." He only becomes "acting Governor" and only until the "recall election is held." And, if Davis resigned, the recall election "will still be held." The only difference is the yes-no question of removing Davis would not appear on the ballot.
As long as California's existing election laws are followed, your scenario is impossible. And since the California Supreme Court has already rejected five challenges to this election, that law will stand.
There is an NAACP/ACLU court challenge to the election that is still live. I just heard the representative for the Plaintiffs in that case on Fox News. She is dumb as a hoe handle. As a 40-year expert in election law, I guarantee that case as well will be thrown out of court.
Rest easy. The only way that Davis can remain Governor is if he wins the recall vote. And his numbers there are already at an all-time low and still dropping. Davis is road kill. Focus your attention on who will replace him from the election.
Billybob
As I understood the laws posted, one only has an "acting Governor" when the sitting Governor is out of state. If he resigns, then by succession, the Lt. Governor becomes (actual) Governor. The recall vote still happens, and if the recall wins, then the candidate (who cannot be the original governor) with the most votes wins. Where things get confusing is whether the former Lt. Governor would go back to being the Lt. Governor, or would be out of office too. That part of the situation does not appear to be clearly addressed in the Constitution or law.