Turboprop pilot reported during departure climb to have penetrated bravo airspace without a clearance.

Narrative

I was issued a VFR departure clearance from SNA; (upon departure; right turn heading 220; climb and maintain 2400ml) I set heading 220 & Alt pre-select of 2400 programmed into the GEC600 autopilot. SNA ground cleared taxi for departure on taxiway A;H;C; hold short of L.Upon reaching the taxiway C/K intersection; was swapped from ground to tower frequency and was immediately instructed to turn left on taxiway L; cross runway 20L; hold short runway 20R. As soon as I crossed the hold bar past 20L was instructed to line up and wait on 20R.Was cleared for takeoff as soon as I entered runway 20R. As I added takeoff power; and began rolling forward; my takeoff clearance was cancelled and I aborted; reduced power to idle and applied brakes. I was instructed to hold position on runway 20R as an airliner was going around right above my position. After the commercial aircraft (I cannot recall which type) initiated their climbing go-around; I was again issued a takeoff clearance from my same position on runway 20R; with a caution wake turbulence advisory. I again initiated a takeoff sequence; climbed off the runway with positive rate; gear up; accelerated; and then flaps retracted. I engaged the autopilot into heading and VS+1000 mode. The aircraft rolled right to intercept heading 220 and continued the climb to 2400ml. A few minutes later I was given own nav from SNA. I initiated a turn to the west/northwest by dialing a heading change with the autopilot heading knob on the G600. I also initiated a step climb by selecting the ALT pre-select to 3400 and setting a VS of +1000 into the autopilot. Climb to 3400 completed. As I exited from under the SNA CHARLIE airspace I again reset the ALT pre-select to my intended cruise altitude of 14500 and had initially planned a right turn towards POM to clear out from under the LA BRAVO. This heading as originally planned would have given me the time and distance to exit under the LA BRAVO heading towards POM with a VS of +1000. On the TCAS traffic screen on the #2 GTN750; I saw a potential traffic conflict with a few targets. I re-engaged the autopilot into a climb and inadvertently pressed the IAS button adjacent to the VS button on the autopilot control which caused the autopilot to climb at a higher rate than anticipated. I used the heading control knob for the autopilot in heading mode to maneuver past and away from the traffic; and along the perimeter of the LA BRAVO south of SLI heading eastbound. I noticed a warning on the map page of the GPS of BRAVO AIRSPACE ABOVE and I saw that I was climbing thru 6900msl. I immediately disconnected the autopilot and attempted to level off; but the aircraft's momentum continued up momentarily before I was able to level off at 6900msl and I may have accidentally entered LA BRAVO airspace by a couple hundred feet. After the correction of altitude and location; I navigated around the adjoining airspace and continued to my destination of ZZZ1. Upon landing I was notified of a possible deviation and called SOCAL TRACON to discuss. After debriefing myself and review of my FOREFLIGHT track data and reflecting on the morning's events; I know that there were a few underlying contributors to this issue. Possible subconscious detractors from the bizarre takeoff clearance cancellation. The decision to depart VFR own nav from a familiar airport I've frequented numerous times in the past. A mistake of pressing the wrong climb mode button on the autopilot during a moment of high pilot workload. Unexpected traffic to avoid along my intended flight path. In hindsight and for future reference; choosing to depart to the southeast as I've typically done in the past; would have avoided this situation. Or filing an IFR flight plan with established instrument departure procedures. The inaction of double confirming the autopilot mode selected before engagement; along with a moment of increased pilot workload allowed an easily preventable mistake to be made. Check and verify. Aviate; navigate; communicate.