"She needs to buy a new bicycle."
Possibly when "newness" is a quality of the thing in question and not related to the awareness of an individual. For example, if my friend has had a bike for three years yet I had until today not seen him/her on it, the newness of the bike would be relevant to my awareness of the bike - not to the three year old bike. 的 would be required when the newness resides in the bike and not when it resides in my awareness. Does this make sense?
Why isn't a measure word needed for "bicycle"?