In this paper, we analyze a certain class of timelike ruled surface in one-parameter hyperbolic dual spherical motions by means of the E. Study map. Then, some new formulae of surfaces theory into Minkowski line space and their geometrical explanations are derived. In addition to that, timelike Pl¨ucker conoid associated with the motion has been obtained and investigated in detail. Finally, we have obtained the necessary and sufficient condition for a timelike ruled surface to be a constant timelike Disteli-axis.