Bonnet cleaning is a term I associate with a rotary floor machine (traditional 175-RPM buffer) and some kind of synthetic fiber pad, or bonnet, like those white rayon or nylon ones with the green stripes across them. As this site deals with orbital/oscillating (OP) machines, we usually talk in terms of "pad" cleaning. A pad is mostly cotton terrycloth, with a far higher level of absorbancy than the synthetic fiber bonnets. A pad may contain some level of synthetic fibers for added strength and durability, but it will be mostly terrycloth cotton.
Pads are usually used damp - immersed in water, then squeezed out either by hand in--or thru a wringer bucket.
I admit I sometimes use them dry, but when I do, I spray my cleaning solution onto the carpet a little more heavily than when I am usuing damp pads. If you are doing a demo for a prospective commercial customer, using the pads dry will result in a much greater visual contrast between the white, unsoiled part of the pad and the part that has been scrubbing the soil out of the carpet.
