In the comics, Batman doesn't die at the hands of Bane. Bane is a powerful adversary, but Batman finds a way to overcome his challenges and live on to fight another day. Their confrontations are epic, but Batman's resilience prevails.
Well, Bane achieves this by outsmarting and overpowering Batman. He uses his raw strength and strategic planning to inflict a severe injury that incapacitates the Dark Knight.
Batman defeats Bane through a combination of physical combat and mental tactics. He trains hard to improve his strength and endurance and then uses his knowledge of Bane's fighting style to gain the upper hand. Also, he sometimes gets help from his allies.
There are some fanfics available. You can start by looking on popular fanfic platforms like Archive of Our Own. However, the quality can vary greatly. Some might focus more on character development, while others could be more action - oriented within the context of their relationship.
Power dynamics are really common. Batman's moral code against Bane's more ruthless nature creates an interesting tension. Also, themes of secrecy and discovery are often there. Since they are from different sides of the law, keeping their relationship a secret and the discovery of it by other characters can be a major plot point. There can also be themes of mutual understanding over time as they get to know each other on a deeper level.