The bearing keeps the clutch plate and inputshaft spinning while applying an axial force (along the input shaft) to keep the clutch plate from touching the flywheel. If the bearing is worn, then you get noises due to the unsmooth movement. When taking off, you are having the bearing having that axial load and then gradually applying the spinning motion as the clutch comes into contact with the flywheel. The combination of load and spinning motion causes the noise. One you fully take your foot off the clutch pedal, the bearing is not subjected to the axial force, and the spinning itself doesn't cause the noise.

Do you keep the clutch pedal pressed down at the traffic lights or anytime you are stopped? Do you rev the engine while you hold the clutch pedal down?