The mode bifurcation between oscillatory motion and no motion of a camphor object floating on surfactant aqueous solution was investigated. The camphor and surfactant were used as the sources of driving and suppressing forces, respectively. A circular plastic sheet was attached to the center of the bottom of a camphor disk, which served as the self-propelled object; further, the contact area between the disk and the solution (S) was varied to control the amount of camphor molecules from the disk that dissolved in the solution. Motion features, that is, the maximum speed, frequency of oscillatory motion, and mode bifurcation, varied depending on S. We discussed the relationship between these motion features and the kinetics of camphor and surfactant molecules around the object. The results suggest that the nature of the oscillatory motion depends on the amount of camphor molecules accumulated at the base of the self-propelled object.