Non-contact, liquid-ejecting bearings (3) are provided for conveying flexible glass sheets (13), such as LCD substrates, at high conveyance speeds, e.g., speeds of 15 meters/minute and above. The operating parameters and physical properties of the bearings satisfy at least one of the following conditions: (a) the average flow rate from the bearing's orifices (22) is in the range of 100-800 milliliters/minute/orifice; (b) the orifices' average horizontal pitch (P) is in the range of 20-55 millimeters; and/or (c) the orifices' average size (e.g., D0) is in the range of 1.0-4.5 millimeters. The bearings (3) can reduce the time-averaged, peak-to-peak variation in the spacing between a LCD substrate (13) traveling at 15 meters/minute and the face (20) of the bearing (3) to less than 100 microns, thus reducing the chances that the bearing (3) will lose control of the substrate (13) or that the substrate (13) will hit the bearing (3).