The lateral migration of bubbles in wall-bounded shear flows arises from the interaction between wall-induced and shear-induced forces, yet the combined effect has remained insufficiently investigated. In this study, we conduct dedicated bubble column experiments with a controlled shear field and wall proximity to investigate the dynamics of single bubbles rising near a vertical wall over a wide range of Eötvös numbers (Eo). In the first stage, we isolate the wall-induced effect under stagnant water conditions: bubble rise velocity is reduced in the vertical direction but enhanced laterally. A wall force coefficient (C_W3) is established that increases linearly with Eo for low-viscosity systems. In the second stage, we examine the combined effect under wall-shear conditions. Two scenarios are considered and evaluated, where the bubbles show distinct behaviors: (i) cooperative cases, where both lateral forces act in concert to enhance migration away from the wall; and (ii) antagonistic cases, where they oppose each other, suppressing lateral motion. This work bridges a long-standing gap in bubbly flow hydrodynamics by providing a closure model that integrates wall and shear contributions in both bounded and unbounded conditions.