There was speculation about the bayonet because information about the victim's head wounds was published before the bayonet was found, and this was such a high profile case. These are the ones that report triangular-shaped wounds, and speculate what the weapon may have been (e.g. a fireplace poker.)
The bayonet was not recovered until more than three days later, and first commented on by police later still. The pathologist who did the autopsy said the wounds were consistent with the bayonet, which has a triangular shaped-pummel. Once the bayonet was found and this was realized, not a lot was said by police about it, possibly because they realized they had already revealed too much.
It was found in the direction of footprints that led from the crime scene in the dew of the lawn and sand of the beach by the first officer to investigate Percy's yard. The footprints led in the direction of ten or so private beaches to the south of Percy's house and disappeared into the water. It was still late summer when the murder happened. In those days, in such a prosperous area, there were large families. One resident said those beaches were often crashed by kids, and used by friends of the families with houses there.
Given that level of use by so many people, the time of year, the location of the weapon (roughly 40 feet out, four down, and 800 feet from Percy's house), the pathologist's comments, and that fact this occurred in a town full of millionaires it seems unlikely the weapon had been where it was found for very long.
As for Thoresen, he was a prime suspect in two other murders in which significant evidence was either found, or said to have been discarded, in water. One was Lake Michigan, the other San Francisco Bay.