Realizing topological superconductors (TSCs) with high transition temperatures (high-Tc) remains a central challenge in the development of fault-tolerant quantum computation. Here, we propose a route for realizing high-Tc TSCs by integrating multigap superconductivity with nontrivial band topology in lithium-doped bilayer borophene. Extensive structural searches and high-throughput screening of over 4000 Li1-xBx nanosheets identify eight promising multigap TSC candidates. Among them, the LiB12 nanosheet is identified as a prototypical three-gap superconductor and simultaneously a topological metal with a symmetry-protected Dirac nodal loop. Fully anisotropic Migdal-Eliashberg calculations reveal cooperative couplings between σ↔in-plane and π↔out-of-plane phonon, which markedly enhance electron-phonon interactions and drive a high-Tc of 57 K. These findings underscore the potential of metal-doped bilayer borophenes as a cutting-edge material platform for achieving high-Tc multigap TSCs.