I've never operated one, but I have worked on alot of American, BE, and Northwest draglines over the years. That said, and it may sound like a stupid question, but when you say it starts to fray 'at the bucket', where exactly are you meaning? Looking at the diagram at the link below, is it fraying right at the becket at the top of the bucket, in the middle of the cable, at the end where it ties in to the chains and the drag cable, or what?
Reason I ask is that, as you know, the bucket dump/trip cable runs through a sheeve. Running in the water is always bad on bearings, and like many draglines I've seen, greasing is not always the operators strong suit. If you just started running this machine then there's no way to know if the sheeve ever got greased properly. If the bearings in the sheeve are dragging or locked up, the sheeve is grooved, etc, etc it can cause problems. In one case the cable is sliding on the sheeve causing the fibers to wear, in the other, a new cable running in a groove that may be even a little but smaller in width than the diameter of the cable will also cause problems by cutting the fibers as the cable is forced into the groove by the weight. In a situation like that it seems like the wear ought to be somewhat spread out along the cable but it could also be even worse at both ends where the cable gets the most stressed from the weight of the bucket reversing directions as it trips.
Beyond that, post a few pics when you get a chance. If what I'm guessing might be going on is off base, the real problem be more evident when you can seeing what is going on.