The big Ugandan, who penned a two-year contract with Amakhosi in September, came on as a late substitute at Charles Mopeli Stadium.
He previously represented the Premiership champions in friendly competition, such as the Macufe Cup.
"When coach (Stuart) Baxter called my name to be in the squad, I felt good because to be included in the squad means it is the first step to get into the starting line-up. I was in the squad the last game we won at FNB when we beat Polokwane City," Bukenya told Chiefs' official website.
"The coach told me that I will be in the squad in the Free State Stars match. I was already focused and ready because I knew the coach would call my name from the bench anytime. I didn’t want to disappoint anyone, the coach, the fans and the management, hence I was focused on the game.
"My first days in the camp have been going very well. I have enjoyed every moment. I shared the room with the funny man, Lorenzo Gordinho. During the dying minutes of the Free State Stars game, coach Baxter called me to dress up. I was very happy because I was waiting for that moment.
"The coach encouraged me to go out to the pitch to win the game for the team. I stepped on the pitch and it didn’t take long for me to be on attack, unfortunately I missed a goal with a header. My head was not down because I knew there are many better chances more to come.
"I was very happy to start with a win. It was good for me and the team. I am now waiting for a turn to start my first game," concluded the former Erbil SC man.