Please see the following two papers for the details of the theory.
1. R. Xu, D. Liang, and L. Shao, Bumblebee black holes in light of Event Horizon Telescope, arXiv: 2302.05671
2. R. Xu, D. Liang, and L. Shao, Static spherical vacuum solutions in the bumblebee gravity model, Phys. Rev. D 107, 024011 (2023)

Units: Geometrized (G=c=1) and the radius of the horizon taken as the unit length
First column: raidal coordinate
Second column: g_{tt}
Third column: g_{rr}
Fourth column: b_t

Specific parameters of each file:
Coupling constant \xi = [0.8045, 1.811, 2.817]8\pi (as the names of the files suggest)
Mass of the solutions = [1.000, 1.000, 1.000]
Bumblebee charge of the solutions = [1.186, 2.986, 4.447]