What's the best way to reset for starter natures?

Now that I have a better understanding of the game I am going to do some form of a challenge run, but would prefer my starter have a decent nature to start out with (either modest delta bulbasaur or mild delta charmander).

What’s the most efficient way to save/reset until I can get the nature I want? can I save in the professor’s building, check their nature in the battle, and reset/try again as required?

Yes, you can save in front of the pokeball of whichever starter you choose.