A very cool idea, but the bullets should probably be slower and loop around in a way that can be predicted by the player so that because it is very difficult not to hit yourself, but also it adds strategy for when the player shoots.
Perhaps instead of the player having infinite bullets, they have a small amount of bullets and can only collect them after they go around the map a few times and slow down.
But besides that, this is a very cool idea that could be incorporated into a full game with a few tweaks.