The point where the string touches the bridge represents a complex nexus of forces. Of course you have the downward force of the string due to the angles created by the string on either side of the bridge. And there are lateral forces created by those angles. Those are static forces because they are always present. There are also dynamic forces caused by the friction of the string on the bridge as the string is tuned which pull the bridge in the direction of the nut. The experienced player will always monitor the position of the bridge, making sure that the feet are flush with the top and the flat side of the bridge is parallel with the ribs.
A common practice is to rub the groove in the bridge with pencil lead, the reasoning being that this lubricates the groove sufficiently for the string to pass across the crown of the bridge. But normally this is not sufficient, and I would recommend certain steps be taken as a string is brought up to pitch for the first time and then from time to time, as part of normal string maintenance
As a new string is brought closer to pitch it is good practice to release the friction point where the string rests on the bridge This is done by pushing up on the string at the bridge so that the string momentarily loses contact with the bridge. This serves to distribute tension equally along the entire length of the string and relieves the build-up of friction between bridge and string. It tightens the knot at the end of the string which is cinched beneath the tailpiece. You will notice a slight drop in pitch whenever you execute this technique, until the string is fully broken in.
This practice also re-balances the lateral forces acting on the bridge and frees the bridge to properly conduct energy to the soundpost/bass bar system of the instrument. The health of any type of string will benefit and it is a good idea to do this from time to time even after the strings have stabilized.
