I would first question why it is thin in the first place.

Was that sodded at one time?

For bermuda, the state of the current grass, and the obstructions to the left and right in the picture, I'd assume it is too shady and no amount of work is going to make the bermuda better.

But if conditions were favorable for bermuda, I'd resod if the rest of my lawn were sodded. Or reseed if the rest of my lawn were started from seed. Whatever would match my current grass. And water.