A method is proposed for the calculation of potential energy curves and related electronic excitation spectra of dopant atoms captured in/on He nanodroplets and is applied to alkali metal atoms. The method requires knowledge of the droplet density distribution at equilibrium (here calculated within a bosonic-He density functional approach) and of a set of valence electron orbitals of the bare dopant atom (here calculated by numeric solution of the Schrodinger equation in a suitably parametrized model potential). The electron helium interaction is added as a perturbation, and potential energy curves are obtained by numeric diagonalization of the resulting Hamiltonian as a function of an effective coordinate z(A) (here the distance between the dopant atom and center of mass of the droplet, resulting in a pseudodiatomic potential). Excitation spectra are calculated for Na in the companion paper as the Franck-Condon factors between the nu = 0 vibrational state in the ground electronic state and excited states of the pseudodiatomic molecule. They agree well with available experimental data, even for highly excited states where a more traditional approach fails.