I'm inclined to think he's telling the absolute truth about what he did to her. I think he pulled her off the pool ladder, and smothered her with the plastic bag, and then dumped her remains. Why else would he say he did that, and tell LE exactly where he put her remains, if it were a lie? If he was trying to cover up a crime he'd say he didn't see where she went, or worse case, he found her in his pool and panicked. He fully admitted to purposely killing her, and told LE where he put her remains that are carefully encased in plastic.
I'm really surprised he had time to even do that, along with make another trip to dispose of the bicycle - this is a little teeny dead end street and by the time he was disposing of her remains, the search had begun. Surely they noticed him driving out of the neighborhood TWICE during the very initial search, the time when the family would be standing in the middle of that road looking up and down the street, asking anyone they encountered had they seen her. That he could load up her remains, and THEN her bike, in full view of the road, is baffling.