核心问题
下面是《英语正误辨析词典》(上海外语教育出版社,1995年版,p.56)对busy用法的正误分析：
“[误] I was busy with writing my term paper last week.
[正] I was busy writing my term paper last week.
[说明]busy后可直接接动名词，不用介词。但如果busy后跟名词时，就要用介词with，例如：He is busy doing his homework.（他忙着做家庭作业。）也可说：He is busy with his homework. busy后如接‘介词+动名词’，这个介词应该是in而不是with。”
您也认为上面的所谓“误句”真是误句吗？
词典解答
我认为上面的所谓“误句”是个正确的英语句子，并没有什么错误。CGEL的作者明确指出：在某些情况下，busy with doing sth. 中的介词是可有可无的：
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Margery is busy writing letters. (CGEL) 马杰里忙着写信。
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I'm busy(with) getting the house redecorated. (CGEL)
我忙于重新装饰房屋。