Q. Is it proper writing to start a sentence using a coordinating conjunction in a quotation? “Her dress is ugly,” said Jane. “But please don’t tell her I said that.”
A. Of course—as long as it reflects the intention of the writer. Your construction indicates a firm pause in Jane’s speech, with the effect that the second half reads like an afterthought. Using a comma and lowercasing “but” could leave open the possibility that Jane spoke without a significant pause, in which case the second half would come across as Jane’s main point: “Her dress is ugly,” said Jane, “but please don’t tell her I said that.”