Could the third character be an oblique, rather than a numeral; thus 68 / 0559?
This would suggest she was moulded in 1968, and the moulding number was 0559 of that year; and that date indicates that she would be a Mk. 1 boat. (Identification points for confirmation of this are visible alloy tubular frames, and stern buoyancy tank athwartships across the boat underneath the stern deck.)
However that does not give the registered hull number (and correct sail number), which for a 1968 Mk 1 boat should be within the range 7002 to 7929. 7002 was the first Mk 1 boat, built in 1967, and 7930 the first Mk 2, built in 1969; and a significant proportion of the numbers in between were issued to wooden (series 1) boats.
There should separately be a plate bearing the registered hull number, bonded onto the GRP, most probably in the usual place (central, where the hog would be on a wooden boat, abaft the centreboard case and underneath the floorboards); however many of them have long since disappeared.
It has been suggested by highly knowledgeable individuals within the GP14 class that the moulding numbers at this time comprised 2 digits for the year, followed by the registered hull number, but that appears not to tally with this number on this boat.
However I also happen to know that Bourne Plastics built a wide variety of other boats, and also car bodies, and my researches into the Privateer 20, backed up by information relating to the Shipmates (two trailer-sailer yachts which they also moulded) rather suggest that after the year code the moulding number appears to have been a sequence across all their mouldings each year, irrespective of which design. That deduction is because the moulding numbers for some of the Privateers and Shipmates are far too high to correspond to the numbers of those boats produced, but would make sense if the sequence covered their entire production of all hulls (and even more sense if the series covered their car bodies as well).
It is all a bit of a mystery, and unless you come up lucky with some detective work I fear that you may not get to the bottom of her identification.
You may be interested in a bit of history of Bourne Plastics; http://www.ournottinghamshire.org.uk/page/bourne_plastics_of_netherfield_langar
Sorry not to be more helpful,
Oliver


