Also, this can be useful if one accidentally strikes a bell louder than intended and needs to bring the volume back down to the same level as the rest of the choir. Pretty much any padded surface can be used. In this case, the waist is often a better option. Table damping is, of course, a creature with its own advantages and disadvantages. All the same, table damping is effective when bells need to be changed for accidentals or whatever.
Table damping the big bells presents a whole new problem, that being whomping.
Press the bell into the pad rather than simply laying the bell down. Lay the bell down, then quickly brush the hand against the casting to kill any residual vibrations.