A Pilot departing from a non towered airport reported they rejected takeoff to avoid a near collision with a corporate jet landing on an intersecting runway.

Narrative

I experienced a near collision with Aircraft X during my takeoff roll from Runway XX at ZZZ. ASOS was reporting winds were variable; and all aircraft had been using Runway XX that afternoon. I departed the parking ramp and taxied south on Taxiway Alpha towards the departure end of Runway XX. As I exited the parking ramp I called out my position on CTAF and declared my intentions to take Runway XX with a departure to the west. I stopped at the departure end; looked for incoming traffic to both Runway XX and XY and seeing none; announced I was taking Runway XX for departure to the west. I put on pitot heat and stall warning heat; checked my landing lights were on; then rolled onto XX and began takeoff. As I began takeoff roll I saw an aircraft above me with landing lights on. It appeared to be approximately 500 ft. and was very near; or perhaps already above the runway; headed south.It appears the aircraft had been making an approach to land Runway XY. I aborted the takeoff and used Beta to come to a stop as quickly as possible; so I could exit the runway. As I pulled back onto taxiway Alpha and turned south again; I could see Aircraft Y; now south of the airport; first banking sharply left eastwards; then executing what appeared to be a 180-degree turn to the right now heading westwards into what appeared to be a modified right base for Runway XX; then a right-hand turn northwards to line up with Runway XX. The aircraft appeared to overshoot Runway XX slightly; but recovered and landed on Runway XX safely. I took two screenshots of the situation shortly before the aircraft landed. This is how I am certain of the aircraft's tail number.I continued taxiing down to the departure end of Runway XX again on Taxiway A; and stopped short of the runway; facing east. I could see Aircraft Y taxiing to the parking ramp. I came on the radio and addressed the aircraft by tail number; and asked if they had heard my calls prior to my takeoff roll. I stated I was concerned that perhaps my radio was not properly transmitting. I heard someone 'mike up' but no response. A few moments later I addressed them by tail number again and asked the question again. This time a voice came on and said that they had not heard my transmissions while they were in the air; but that they could hear me now while they were on the ground. I re-accomplished my takeoff checks and departed using Runway XX. About 20 miles to the west I called up Center and picked up VFR flight following back to ZZZ1; at 16;500 ft. I asked the controller if they could hear my radio OK; and they said they heard it '5 by 5.' I am left with the impression that the pilot of Aircraft Y was in a hurry and may not have been on CTAF frequency while airborne; or at least were not on frequency until very shortly before attempting landing. I did not hear them call out intentions to land at all; and I did not hear anything from them until after they had passed overhead and declared their intention to turn around and land on Runway XX. The relatively aggressive maneuver I saw them execute south of the airport; rapidly turning around and landing on Runway XX; rather than orbiting a safe distance to the south and clarifying the situation; and clarifying that the runway was now clear and safe to land; surprised me.As for my own actions I have ADSB-in in my avionics; which is fed by Bluetooth to my iPad. I did not see depiction of an aircraft prior to my first takeoff attempt. Also when I looked northward prior to entering the runway I did not see Aircraft Y. I am not sure why this was. I am not sure whether they had their landing lights on until immediately prior to the landing approach; at which time I was already rolling for takeoff in the opposite direction. The grey skies to the north probably made their aircraft a little more difficult to see; particularly if they did not have landing lights on; or if perhaps they executed a sharp right or left base to final for Runway XY; of the same manner they did on Runway XX immediately following the near collision incidence. If this were the case; I would not have seen their landing lights as the lights would have been pointed perpendicular to the runway heading.As for what could be done to prevent recurrence; a note on ASOS that the calm wind runway is Runway XX would be helpful. What really could be done is for pilots to exercise radio discipline and properly announce their position and intentions when approaching an airport and to listen to others doing the same.