A search shows one solitary thread on bgreek that uses the keyword "Twitter" in relation to tweeting in Greek (gweeting?) (That would be Μάρκoς, needless to say.)
I follow @DailyKoine (random verse now and then), but otherwise haven't seen much that's relevant. The hashtag #Koine is dead, and #AncientGreek is quiet (though I just answered a simple qn for someone). Nothing on the hashtag #BGreek.
Who else uses Twitter? Anyone want to help adopt #Koine?
My own twitter account is @eukras.