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The patch is good. 
I was first surprised by the fact that e.characters_written is not used
in the write() method; but _flush_unlocked() already adjusts the
_write_buf according to the original e.characters_written raised by the
underlying raw file. Everything is fine.
I suggest however to add some tests around the first "except
BlockingIOError". This would answer the question:
 # XXX Why not just let the exception pass through?
For example, I modified a function in your patch:
 def testWriteNonBlockingOverage(self):
 raw = MockNonBlockWriterIO((-1, -2))
 [...]
 # Subsequent calls to write() try to flush the raw file.
 try:
 bufio.write(b"x")
 except io.BlockingIOError as e:
 # Two more chars were written at the raw level
 self.assertEqual(bufio._write_buf, write_buf[2:])
 # But write() did not accept anything.
 self.assertEqual(e.characters_written, 0)
 else:
 self.fail("BlockingIOError not raised")