Translation:She needs to buy a new bicycle.
The suggested answer for the rejected answer "She has to buy a new bicycle." is the grammatically incorrect English sentence "She have to buy a new bicycle."
"She wants to buy a new bicycle" still not accepted. Reported 26th October 2018.
自行車 腳踏車 We both understand, the same. In China I think they say 自行車, but it doesn't confuse them when you say 腳踏車.
In Taiwanese, we also call bicycle 鐵馬. But only in Taiwan, in other places they won't understand.
Yeah 铁马 would take some deciphering for Mandarin speakers... Another term for bicycle is 单车/單車. I thought it originated in Taiwan, but I don't know if it's still used there (EDIT: Looks like it is according to @FuCnSW 's comment below). It gains popularity in mainland China thanks to the bikeshare services/apps, which are called 共享单车 instead of 共享自行车, apparently because the former is more concise and perhaps more stylish.
Actually I did learn it in school as a 修辞手法. I think it was 借代 but I can't say for sure, please enlighten me if you know.
I think it's just a metaphor (比喻), comparing a bicycle to an iron horse. I looked up 借代 (known in English as synecdoche) and I believe it's something else, e.g. in I read Shakespeare, "Shakespeare" is used in place of "Shakespeare's works."
It's not a 比喻, because I remember everyone in class answering that and the teacher saying it was something else, but that's where it becomes unclear because it apparently didn't make sense to all of us so we had a huge debate and noted it down as "to remember for exams".