The Egypt striker, who is on loan from Zamalek, infuriated Bruce after returning late from international duty following Egypt's draw with Zambia in the World Cup qualifiers.
But after holding a clear-the-air meeting with Bruce, Zaki is convinced he can now put troubles behind him and focus on helping Wigan claim a European place.
"I clarified many things to Bruce," the 26-year-old told Al-Hayat TV.
"He understood my reasons for staying in Egypt during the past week but told me I should have returned immediately to England after the Zambia match.
"He wanted my hamstring injury to be assessed by Wigan medics. I apologized to him and we ended up laughing.
"I may return to training after a week. I'm determined to do my best in the remaining Premier League matches."
Wigan lie eighth in the league table with 41 points. A seventh-place finish would be enough for them to play in the Europa League, the new version of the UEFA Cup.