From TalkBass Wiki
Ferruls, or Bass String Ferrules, are small cylindrical metal grommets which 'cap' the holes made through the basses body for string-through-body bridges. Their function is to 'hold' the ball of the strings from travelling through the holes, thus clamping the ball end to the bass, to prevent against wear and tare at the holes edges, and to increase the general aesthetics of the bass.
Typical dimensions are:
