That clause almost certainly means that she wouldn’t be able to claim back the milage which she would be able to claim tax free under HMRC rules for using her own bike for work purposes.
If you use your own car for company business you can claim iirc 40p per mile tax free. Same applies if you use your own bike although the amount is a lot less. As the bike is owned by the company you wouldn’t be able to claim this. There shouldn’t be an issue with using the car and claiming milage back.
Sorry, that sounds quite unclear but I hope it helps!