Interaction between local magnetization and conduction electrons is responsible for a variety of phenomena in magnetic materials. It has been recently shown that spin current and associated electric voltage can be induced by magnetization that depends on both time and space. This effect, called spinmotive force, provides for a powerful tool for exploring the dynamics and the nature of magnetic textures, as well as a new source for electromotive force. Here we theoretically demonstrate the generation of electric voltages in magnetic bubble array systems subjected to a magnetic field gradient. It is shown by deriving expressions for the electric voltages that the present system offers a direct measure of phenomenological parameter β that describes non-adiabaticity in the current induced magnetization dynamics. This spinmotive force opens a door for new types of spintronic devices that exploit the field-gradient.