Below are the links to explanation from 국립국어원. The root word is 바라다, not 바래다.
Hence, it should be like "감기 빨리 낫기를 바라요."
But honestly, "바래요" is used so much more often than "바라요" that the latter sounds wrong instead...
Anyways, 앞으로는 "바라요" 사용하기를 바래...ooops.. I mean 바라요.
http://krdic.naver.com/detail.nhn?docid=15142100
http://www.korean.go.kr/09_new/minwon/qna_view.jsp?idx=51176
http://www.korean.go.kr/09_new/minwon/qna_view.jsp?idx=46283