Climb into the attic and walk over to where the roof meets the outside wall nearest the bathroom.
Drill a reference hole down through the soffit, the underside of the roof, halfway between the wall and the ends of the rafters. Leave the attic.
Locate the reference hole from outside the house and set a ladder beneath it. Replace your drill bit with a hole saw. Climb to the soffit and center the hole saw over the reference hole. Cut a hole through the soffit. Climb down and replace the hole saw with a screw bit.
Attach a 12-inch duct connector to the wall cap with foil duct tape. Insert the connector through the hole and push until the wall cap is against the soffit. Drive screws through the screw holes to attach the wall cap to the soffit. Squeeze a bead of caulk on the seam between the wall cap and soffit.
Climb back into the attic. Place a 90-degree elbow on the connector duct and secure it with foil duct tape. Slip the end of the vent duct to the other end of the elbow and secure it with foil duct tape.