Single engine pilot reported causing a critical ground conflict.

Narrative

Aircraft X taxied out to the run-up area at what we call Taxiway 1 South. Runup was performed; then ATIS was picked up; and then clearance delivery for an IFR clearance to ZZZ1. Clearance was read back and confirmed by the co-pilot who was operating the radios for me.We then called up ground; which we are told to use on that side of the airport. We told ground control that we were ready to taxi. Taxi instructions were given to us: Taxi on Taxiway 2; cross RWY XX to RWY XY. The taxi instructions were read back to the ground controller.We were aware that the ground controller was talking to two military jets at the end of RWY XZ and had asked them if they wanted to communicate on UHF or VHF. I thought that; because military jets were waiting to take off on RWY XZ; the ground/tower had switched the active runway from RWY XY to RWY XZ.I proceeded to go past the hold line; and as I entered onto RWY XY from Taxiway 1; we noticed a jet touching down. I immediately applied hard braking to stop the airplane. The jet went to the right side of the runway. I estimate the distance between us to be more than 25 feet.Ground then asked me to state our position; to which I told them Taxiway 1 South; which was our initial to ground.At no time was I asked to call; write down a number; or issued any warning; or asked what took place. At no time did the ground or tower tell us to stop while taxing out. The jet later reported to me that they were calling us on the tower frequency. The jet called the tower and asked them to save the tapes. We taxied as instructed; remained on frequency; and; at the end of Taxiway 2/RWY XY; switched to tower and took off.