General aviation pilot reported turning incorrectly on a taxiway and crossed an active runway without clearance. The pilot contacted ATC for further clearance to the FBO.

Narrative

Following a VFR landing into ZZZ on Runway XX; I exited at [Taxiway] 1 and contacted ground. The controller gave taxi instructions to the FBO but he spoke so fast that I could not understand him at all. I asked him repeat the instructions and to please speak slowly. He repeated the instructions to taxi along Taxiway 2 and turn on 3 to the FBO. Again; he spoke fairly quickly though I thought I understood him. As I taxied along southeast along Taxiway 3; I saw FBOs to my left; which is where I thought my requested FBO was. Having heard a clearance to FBO in his taxi instructions; I turned toward the FBOs. When I approached Runway XX; I looked to my right and saw an aircraft on final which appeared to be around four or five miles out. Believing I was cleared to the FBO and that it was safe to cross; I proceeded to the east side of the runway. Seconds later I was informed by ground control of a possible deviation and that I was instructed to turn RIGHT on [Taxiway] 2 not LEFT. I realized then that the FBO I requested was in fact on the WEST side of the runway. The controller pointed me toward; and cleared me; to taxi to the correct FBO. In retrospect I believe several things went wrong; mostly on my part. The few times I have been to ZZZ; I bought fuel at an FBO on the EAST side of Runway XX. The controller spoke so fast that I didn't get any of it; and even after asking him to speak slowly; he spoke fast; but somewhat slower; and I believed I understood him; Because I remembered that the FBO was on the East side; and because I believed I was cleared to the FBO; I crossed Runway XX and was quickly informed of a possible pilot deviation. The above represents what I did wrong. My planning of exactly where the FBO was should have better; not relying on memory. The crossing of an active runway; even believing I was cleared to the FBO should have rung bells. Seeing traffic a safe distance away I crossed. I remember slowing at the runway; thinking maybe I should confirm; but let it go knowing that the landing traffic was far off and the controller knew what he was doing.What I learned and will change: Do not continue taxiing as the controller is giving me my complete instructions; I made the left turn onto [Taxiway] 3 as instructed before he finished. I should have waited until the instructions were clear to me; I should have asked him to repeat a third time; so no mistakes were made when transcribing. In the future I will not begin my ground taxi during the readout. I tend to do this at home airports which are smaller and more familiar. ZZZ is a busy airport. I usually stay close to home in my area. Things always happen faster there; and flying single pilot is probably not the best choice for going there. On the few trips I make there yearly. I will try to take a second pilot with me. Lastly; I would like to say that the controller truly should have spoken slow enough for a pilot to understand the first time. Perhaps the local pilots understand better when controllers talk fast because they are used to it. But this is not good for folks who speak slower. In this particular case the interaction definitely made me somewhat nervous. My mindset during the taxi was definitely rankled after the first and second taxi instructions that were given; once way too fast; and the second just fast. I should have stopped and collected myself.