The three-dimensional flow around a spherical clean bubble translating steadily in a wall-bounded linear shear flow is studied numerically. The present work is concerned with the drag and lift forces experienced by the bubble over a wide range of Reynolds number (0.1 ≤ Re ≤ 103, Re being based on the bubble diameter and relative velocity with respect to the ambient fluid), wall distance (1.5 ≤ LR ≤ 8, LR being the distance from the bubble center to the wall normalized by the bubble radius), and relative shear rate (−0.5 ≤ Sr ≤ 0.5, Sr being the ratio between the velocity difference across the bubble and the relative velocity). Based on the above range of parameters, situations where the bubble is repelled from or attracted to the wall are both covered. The flow structure and vorticity field are analyzed to obtain qualitative insight into the interaction mechanisms at work. The drag and lift forces are computed as well. Their variations agree well with theoretical predictions available in the limit of low-but-finite Reynolds number and, when the fluid is at rest, in the potential flow limit. Numerical results and analytical expressions are combined to provide accurate semi-empirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance.