A rolling bearing apparatus includes a first machine element, a second machine element, a rolling bearing, a seal, and a bypass device forming an electrical connection between the first machine element and the second machine element. The rolling bearing has an axially aligned axis of rotation, a first bearing ring, a second bearing ring arranged concentric to the first bearing ring on the axis of rotation and fastened to the first machine element, and rolling elements arranged radially between the first bearing ring and the second bearing ring. The seal is arranged radially between the first bearing ring and the second bearing ring. The bypass device has an electrically conductive bypass conductor formed from loop-shaped stitched fibers and a holder holding the bypass conductor in an electrically conductive manner. The holder is fastened to the second bearing ring radially between the first machine element and the second bearing ring.