She WAS tied to Bowser in secret. She was perfectly content with their little live-action roleplay, with sexing and dating Bowser behind closed doors; reveling and rejoicing in the chaos and destruction which resulted from her sex-fueled vacations with her real man.
And then Bowser tried to woo Princess Peach right in front of Mario. Which would have been fine if Peach had not broken character, had she not revealed her TRUE feelings for the Koopa King right in front of Mario, thus sending our intrepid plumber into desperation mode and starting a panicked chain reaction in which BOTH suitors would lose Princess Peach forever.
Not that Mario ever had Princess Peach to begin with (spoilers, he didn't). But once Peach shouted, "ENOUGH!!!" That was it. Whatever tiny chance he ever had of winning the girl was destroyed right then and there. Mario has been an incel loser with the ladies ever since.