How can I re-select the starting bonus when restarting a campaign scenario?

It is generally not recommended to restart a scenario using the "Restart Scenario" ("Start Over") button in the game menu, as it may trigger a known bug where the game fails to reset the visited status of tents (if they are present in the scenario and have already been visited).
I would suggest saving the game more frequently and using different file names instead of a system like "this_save" and "that_save."
Also, it is important to note that after successfully completing a scenario or an entire campaign, you will be prompted to save the game. This is not accidental, and you should do so. Some bonus campaigns become available only after completing several initial campaigns, and the game determines this based on the information in the save file. (I wrote this from memory, as I haven't played campaigns for many years)