Even though I would normally agree with what Gices has already said, I must point out that your daughter could actually get a discount when taking out a car insurance policy. If she had not made any claims during that year this would lead to a 1 year NCD for bikes. I personally know that companies such as: Tesco, Direct Line, or Churchill will accept NCD earned on a bike policy and will therefore be able to offer discounts on their car policies. I hope this helps.
Jacob,
You are right - your bike no claims bonus can be transferred to a car insurance policy (fully or partially) but I'm not so sure about NCB earned for a scooter. I may be wrong and the only way to find out is to get in touch with the companies you mentioned and ask. So Duncan, to make sure that your daughter does not miss out on any possible discounts, you are better off contacting the 3 companies listed above and see whether the scooter NCD can be applied to your daughter's car insurance premiums.
Try carol nash which is a motorcyle insurer which also gives ncb on cars.