Maybe I'm not being clear. I do not think / assume she walked to the park at all. I think it highly unlikely that she'd have set off from that bench on foot without at least one camera picking her up.
We've been told she was last seen near a bench at 12.09.
From then I've merely reacted to suggestions that she's probably in water somewhere and I'm trying to figure out how that would feasibly happen of her own volition from that bench.
If PR started to give her a lift home, even if he dropped her somewhere along the way for whatever reason, I can't see her getting to the park without being seen. It's a quick trip around the corner to her home. I personally think she'd have been found.
The water courses near to her home have been searched. On a much earlier thread somebody said it would be unlikely that she get far in water from there.
So if she did get to the park and from there to the river or pond my assumption is somebody gave her a lift. It might be wrong.
So no, I don't think she walked to the park.