If we were the original game designers, there would be at least three options for handling this situation:
1. The owner can bid on their own player, and the time will not be reset after buying the player back.
2. The owner can bid on their own player, and the time will be reset after buying the player back.
3. The owner cannot bid on their own player.
In my opinion, option two is more flexible and has no real problems. It is the more ideal option.