It said its regional bus network was seeing passenger numbers at 65-70% of typical levels on most days and at 80% in some regions - up from around 20% in March.
Go-Ahead said it was due to "pent-up demand" for leisure, retail and socialising.
The group said the increase in bus passenger numbers would mean its reliance on government subsidies to keep services operating during the pandemic would reduce.
Go-Ahead, which also operates the Govia Thameslink and Southeastern rail franchises, said it was enjoying "robust trading" across all of its divisions.
Chief executive David Brown said: "After more than a year of COVID-19 restrictions limiting travel, it is great to see our buses and trains carrying more passengers as these restrictions start to ease and people enjoy the benefits of communities and businesses reopening.
"There are more people using our services today than at any point over the pandemic and we are ready to safely welcome more people back to our buses and trains.
"As we emerge from the pandemic, public transport has a huge role to play in economic recovery; and an equally important role in tackling climate change as we encourage more people onto our services and away from private cars."
Go-Ahead said that its overall financial outlook for the year ending 3 July had improved, thanks to an increase in expectations for its London and international bus division.
Last week, figures from the Office of Rail and Road showed passenger journeys on Britain's railways in the year to March had fallen to the lowest level since 1872.