Regarding the question, what you have written is OK.
However, the expression 'drop me a line' usually refers to calling someone over the phone rather than writing.
Also, 'about your news' is OK, although it gives a feeling that something special or important has happened to that person and you want to know more details. Therefore, some other expressions might be as follows:
-Please let me know what you have been doing recently.
-I am interested to know what you have been up to recently/since we last spoke.