Just a thought
If use of motorbike is say 80:20 business to private
Claim VAT through company
Have full Capital Allowance
Most expenses through company so get VAT back on fuel, servicing, spare parts etc (exception being parking and tolls and fines arising from private use).
Keep a log and pay 24p per mile of private use back to company
In other words the mirror image of owning bike privately and being paid 24p/mile for business use.