Mr Bliss was always a very secretive man and would most likely have wanted to keep that fact a secret from everyone he knew.
I also suspect that he thought that by telling them that he was a double agent they may have acted differently and this would make serpine suspect him. Telling the Elder's would have also been a bad idea as there has always been a history of the Elder's doing the wrong thing when given news of events.
Mr. Bliss uses the fact that only he knows he's a double agent to gain Serpine's trust when he pushes Skulduggery off the cliff in an attempt to kill him. He would have then reported this back to Serpine and this is turn would lead to
"his actions would become predictable"
But considering the lack of background we gain about Mr.Bliss apart from the fact that he is strong and brother of China we have no way of knowing why he didn't tell anyone.