GA pilot reported a near miss with an airliner while on an ATC assigned heading and altitude and took evasive action to avoid a possible collision.

Narrative

I was cleared through San Francisco's class Bravo at 3;500ft along the coast. I was cruising southbound over the southern end of the San Francisco coast in the Bravo airspace at an assigned altitude of 3;500; when ATC issues instructions to me to look for traffic - a large airliner that had just departed from SFO.I start scanning for traffic and identify a target on my ADS-B on a converging course; below us and climbing. At no point do I tell ATC that the traffic is in sight; though I continue scanning. The target continues converging on our course. I then receive a traffic warning that the target is now 500ft below us from my ADS-B in and finally spot the traffic converging on our position from below us at our 9 oclock on a collision course. I disengage my autopilot and climb. The airliner passed closely below us while I was at an altitude of approximately 3;700. I estimate we were 300-400 of vertical distance and 0ft of horizontal distance; which meant if I stayed at my assigned altitude of 3;500 we may have been on a collision course.I'm filing this incident because both of us were in class bravo airspace on assigned altitudes and courses; and at no point did I call them in sight nor do I recall the airliner calling us in sight; nor were we given warnings or instructions to deviate from our course for traffic avoidance.