GA pilot reported they flew into Class B airspace without a clearance.

Narrative

I was flying a new aircraft that I purchased 3 days ago. I was out practicing in the NW region of Houston planning to practice stalls; steep turns; and learn the avionics of the new-to-me aircraft. While I was working on the aircraft maneuvers and other scenarios; I started focusing on my auto-pilot as it kept disconnecting. I focused in on the auto-pilot and got completely distracted by it. I was focused on my altitude and heading; but not my airspace situation. I looked up and realized immediately that I was east of Houston Executive Airport (TME). I quickly changed course; turning right to a southwesterly heading in an effort to quickly depart the airspace and while creating minimal diversions for incoming aircraft to IAH. After I was out of the airspace; I contacted Houston approach on 123.80 and self-reported my erroneous flight into Bravo airspace at about 5;000 ft. NW of the Houston IAH airport. The Controller explained that I had a possible pilot deviation and that I needed to copy a phone number; and contacted the folks at that number as soon as possible. I advised I would land the aircraft and call. This is a first time incursion for me; and I feel awful for the potential additional work I put on the Controller as he may have had to move incoming aircraft around me.