Vibrato is an expressive technique used by string players and achieved by slightly shading the pitch alternately sharp and flat at varying speeds and widths, while keeping the pitch focused and not distorted to the point of becoming unrecognizable.
On the bass, vibrato is created by swinging the forearm from the elbow down toward the bridge and back toward the scroll, using the wrist as a guide and the finger on the string as the pivot point. This motion should be very smooth and should be done with a great amount of control. A mature player will never let his/her arm swing wildly and uncontrolled.
The hand should remain flexible, and the student should not clutch the neck while vibrating. Clutching will only make the vibrato very narrow and difficult to control.
Always keep your fingers curved. Remember there is strength in arches.
While vibrating, it is important, especially for a beginner, to maintain a proper hand shape with all of the necessary fingers down, while focusing most of the weight on the finger which is being used to play the note. This is true even in thumb position and is very important for many reasons, such as accurate shifting, intonation, and control of vibrato. The only exception is to occasionally lift the first finger while vibrating on the fourth finger to allow for a wider vibrato if the music calls for it.