Leave from the door you just opened and go to your left, head into the maze. Go left always in the maze unless your only option is to go right. When you get to the back of the maze you will see a brick wall, look down the hall and you will see two openings. Take the first opening to the right and fall into the hole. Then go to the end of the hall and jump out, push the button on the wall and you will see a cinema of the door opening back in the house. This door is timed, so you have to be fast.
Go back the way you came in, jump out of the hole and go left. Then keep following the maze turning right everytime unless you have to turn left.
Exit the maze at the end and run back into the house and through the door. It leads to the basement below, where you'll you will see several chests and windows on each side. It looks like a huge statue is on the right.
Note: When you find the lever that you have to pull to access the secret room, be sure to take the flares on the right hand side. It'll make the journey back much easier.
Actually, you don't need the Detonator Key to complete Bartoli's Hideout. Go to the left side of the white building you are supposed to blow up. Hold the Action button and press Up. You should vault up the roof. Find the hole, drop down and exit.