选B
比较stop doing sth 和 stop to do sth
stop doing sth.意为“停止做某事”即“不做某事了”,如：
He stopped watching TV and began to read English.他停下来看电视,开始读英语.
stop to do sth.意为“停下来原来做的事,做下面的事”,如：
He watched TV for an hour; At 8 he stopped to do his homework.
他看了一个小时的电视,八点钟他停下来(看电视)去做作业.
而句中 We’re listening to the news.可知该选择B