Bismuth thin films constitute a promising nanostructure for the fabrication of spin-based devices. To achieve this goal, it is necessary to obtain high-quality Bi layers with controlled and reproducible properties. Therefore, studies focused on the understanding of the nucleation process and the correlation between the growth conditions and the film properties are of great interest. In this work, we have studied the electrodeposition of Bi thin films onto GaAs(111)B substrates at different overpotentials. In Part I, we have analyzed the nucleation of the films by means of potentiostatic curves. The current density transients have been deconvoluted into individual processes taking into account the energy band diagram of the semiconductor-electrolyte interface. The deconvolution of the current density transients indicates that Bi electrodeposition follows a 3D nucleation controlled by diffusion, accompanied by concurrent processes such as both proton adsorption and reduction. The competition of these processes is controlled by the energy distribution of the surface states at the semiconductor-electrolyte interface and determines the nucleation process. The correlation between the properties of the Bi films and the Bi/GaAs interface with the nucleation process, i.e., with overpotential, is discussed in detail in Part II of this work.