If they're not a proximal cause, no. If they are, yes.
But if ridership is going up even whilst prices are offensively high, satisfaction is at an all-time low, and reliability is a joke, then you can't assert that ridership is going up because of privatisation, it's more despite privatisation because people have few other options (cf London where driving is slow because of congestion, buses are often stuck in the same congestion, cycling is still sketchy in some parts, high prices have forced people out of walking distance, etc.)
If they're not a proximal cause, no. If they are, yes.
But if ridership is going up even whilst prices are offensively high, satisfaction is at an all-time low, and reliability is a joke, then you can't assert that ridership is going up because of privatisation, it's more despite privatisation because people have few other options (cf London where driving is slow because of congestion, buses are often stuck in the same congestion, cycling is still sketchy in some parts, high prices have forced people out of walking distance, etc.)