I used to live in MK. You would not get very far without being captured on cctv, definitely not to the bletchley area from furzton.
If she went into furzton lake of her own accord that morning, I think she or her backpack would have been found when they searched it.
The body of water is big and it’s not clear so it could take a long time to find it. We don’t know what she had in her bag but it either could have weighed her down, or more likely someone took it when it was left at the lakeside and never realised it was significant.