I have limited knowledge of tennis ticketing, but I think there are all day ground passes? You could say something along the lines of “I was thinking of getting a pass, if we went on the same day we could meet up for a drink while we are there”. That would give you both limited pressure, the option for both of you to limit or extend the time depending on how things go, and also makes sure you don’t get stuck in a position of sounding like you are offering to pay for an expensive tennis ticket for her.