  We identify a magnetic field induced transition from a vortex liquid to Bose
metal in a 2-dimensional amorphous superconductor, a-MoGe, using a combination
of magnetotransport and scanning tunnelling spectroscopy (STS). Below the
superconducting transition, Tc ~ 1.36 K, the magnetoresistance isotherms cross
at a nearly temperature independent magnetic field, H_c^*~ 36 kOe. Above this
field, the temperature coefficient of resistance is weakly negative, but the
resistance remains finite as T --> 0, as expected in a bad metal. From STS
conductance maps at 450 mK we observe a very disordered vortex lattice at very
low fields that melts into a vortex liquid above 3 kOe. Up to H_c^* the
tunnelling spectra display superconducting gap and coherence peak over a broad
background caused by electron-electron interactions, as expected in a vortex
liquid. However, above H_c^* the tunnelling spectra continue to display the gap
but the coherence peak gets completely suppressed, suggesting that Cooper pairs
lose their phase coherence. We conclude that H_c^* demarcates a transition from
a vortex liquid to Bose metal, that eventually transforms to a regular metal at
a higher field H* where the gap vanishes in the electronic spectrum.
