Somehow bringing the Bunny so close to that door (that's why he kept messing around with it in the doorways) can bump Mario into that room. The bunny doesn't disappear and when he somehow managed to grab the bunny through the door to bring him to the Bowser Basement Door it looks like it pushed him into the room. I can't remember ever reading about this, but once he got the key from the Fire Sea it didn't matter that he didn't have enough stars, he could go to the 2nd Floor and do that crazy Backwards Long Jump trick (that freaked me out, when he got into the Clock Room without getting those stars!)

Going down the slide was awesome, as was the jumping through the floor to skip running up the stairs to the 2nd Floor. Must have taken him tons of time to master...