Just had this back from The embassy:
Dear Mr Clancy
You are allowed to buy a car or a motorcycle in Turkey if you wish to export. If you wish to buy and ride your motorbike in Turkey you must register your motorbike with the local traffic police. The local police would ask you to submit your residency permit.
Therefore, you need a residency in order to buy and ride your motorbike in Turkey.
Yours sincerely
S RAMADAN
Secretary
Turkish Embassy
Office of the Financial Counsellor
43 Belgrave Square
London SW1X 8PA
Tel: +44 20 7245 6318