How much knowledge do they have on each other? Is it only that they have an enemy to defeat or do they know who they are up against?
He can only turn this into an inconclusive with a suicide but it's unlikely that Nagito will pull a suicide that early, not until he knows that he can't defeat his enemy. Just like what he did in Super Danganronpa 2.5. Unless he knows, he'll pull a suicide right away. It will also be in Batman's favor depending on their knowledge on each other, since he has prep.
The only thing I can think of here is it depends on their current knowledge on each other
Two Scenarios:
If they don't know each other, Batman won't probably be able to brace himself against the bullet ricochet even with a prep but who cares if he is braced for it or not, the bullets are irrelevant at this point and Batman could possibly survive them with ease (even if he's prepared for it or not, specially with that durability) and Nagito's suicide will likely be pulled later instead but it will definitely happen and it will be inconclusive.
If they do know each other, Nagito tries to pull a suicide right ahead and Batman will likely survive because he has prep but I don't know what kind of prep would it be. Batman wins on this possibility.
Another Possibility:
Batman can also win in if both of them survives the explosion of the setting. Due to Batman being able to survive situations which would kill an average human and Nagito survived with his extreme luck. Then, Batman will win with his combat experience in the aftermath.
TL;DR
If they don't have knowledge of each other, Inconclusive.
If they have knowledge of each other, Batman or Inconclusive.
I can't really see Nagito winning either way because he has no experience in combat and he only relies on his luck, preparations and intelligence. I also don't know why I thought of Nagito's suicide the moment I saw "grenade" and "explosives factory". He's just really the type of person to suicide and also don't question me why I thought of his suicide the moment I saw grenade and an explosive setting.
- EDIT: Nagito can only win IF he has prep and they don't have knowledge of each other. He can wish for his luck to be able to kill his "opponent" in any ways or by throwing a grenade and he survives the explosion with his luck somehow with a very high chance due to his prep, as vague as that sounds, that was actually the way how Nagito made the "traitor" a murderer/killer of the second to the last Class Trial in Danganronpa 2 Chapter 5.

Oh boy, I wonder what will happen?