"Can we take a bus to the school?"
Nope, that would imply that you're going to school to catch the bus. Also, without the "吗" at the end you're making a statement rather than asking a question
我们 = we 可以 = possibly/can 坐 = by means of (lit: "sitting") 公共汽车 = bus 去 = go 学校 = school 吗 = (question marker for yes/no-answer questions)
Saying 坐公共汽车at the end is grammatically most correct.... The answer sentence here is structured poorly.
Word structure is wrong, the suggestion from Dalton Stout is actually the correct grammatical way to structure the sentence, the answer here is incorrect.