Busch was parked by NASCAR officials after intentionally crashing into the back of Truck series title contender Ron Hornaday under caution, spinning him against the barrier and putting him out of Friday night's race.
His actions came as retaliation for previous contact while fighting for second place early in the race.
On Saturday NASCAR announced Busch had been suspended from driving at Texas for the reminder of the weekend, forcing him to miss both the Nationwide and Cup Series races.
"I've had a lot of time today to sit and reflect, and try to put my thoughts into words as best I can," read an open apology letter issued by Busch on Saturday night.
"I want to sincerely apologise for my actions during Friday night's Truck Series race at Texas.
"I apologise to my fans, all my sponsors, everyone at Joe Gibbs Racing and Kyle Busch Motorsports.
"After talking with my team, it's great to have their support and encouragement to assure me that there are better days ahead. Even though this took place while driving for Kyle Busch Motorsports, I am sorry for how difficult this has been for everyone associated with Joe Gibbs Racing's Nationwide and Sprint Cup Series teams.
"I'd also like to apologise to Ron Hornaday Jr, and everyone associated with the #33 team in the Truck Series.
"I understand why I was taken out of the car for the rest of the weekend. NASCAR officials had to act, and I accept their punishment and take full responsibility for my actions.
"As a racecar driver, the hardest thing to do is to sit on the sidelines listening to cars on the track when you know you should be out there competing. For this, I have no one to blame but myself.
"Through a lot of support from the people around me, I feel like I've made a lot of strides this year, but this was certainly a step backward. Moving forward, I will do everything I possibly can to represent everyone involved in a positive manner.
"However, I know my long-term actions will have more of a bearing than anything I say right now."
NASCAR president Mike Helton said further penalties for Busch were possible, while the driver's boss Joe Gibbs would not confirm whether the team was considering taking any internal measures.
"I think right now we're just trying to handle the first things first for us and there's so many things to consider and so many people to meet with," Gibbs said. "I think we're still early in the process and we're trying to work our way through it as best and as fast as we can."
Following Gibbs' remarks, Toyota issued a statement saying it trusts JGR will handle the difficult situation properly.
"Toyota understands it is NASCAR's responsibility to enforce their rules for the well-being of the sport," the statement read.
"We recognise this is a difficult situation for both Joe Gibbs Racing and Kyle Busch with respect to the incident that occurred at Texas Motor Speedway during Friday night's NASCAR Camping World Truck Series race.
"However, we are confident in the leadership of Joe and JD Gibbs, and are certain the team will handle this difficult situation in an appropriate manner. Toyota remains 100 per cent committed to its support of Joe Gibbs Racing and its drivers."
Busch has all but lost any chance of contending for the Cup title as he will not be able to score points for the Chase this weekend, with only two more races left in the championship.
