We deposited amorphous Bi films with a thickness between 3 and 6.5 nm at 4.2 K on top of previously deposited Co clusters having a mean size of ∼4.5 nm. The Co cluster layers thickness was between 2.3 and 5 nm. In-situ electrical transport measurements were performed between 2 and 100 K. Measurements on as-prepared samples having a Bi layer thickness of 3.0 nm show hopping (tunneling) conductivity as σ(T) = σ0 exp[-(T0/T )1/2] above the superconducting transition temperature TC and re-entrance behavior again with hopping (tunneling) conductivity below TC. Annealing of films having a Bi layer thickness of 5.5 nm results in a decrease of resistivity, with variable range hopping conduction behavior as σ(T) = σ0 exp[-(T0/T )1/3]. Quite different are the findings for films having a Bi layer thickness of 6.5 nm: Annealing of these films results in a power law behavior as σ(T) = σ0Tα with α = 2/3, indicating that these films are close to a quantum critical point separating superconducting and insulating phases. A phase diagram including all experimental observations is proposed. © EDP Sciences, Societ̀a Italiana di Fisica, Springer Verlag 2013.