If the Chief Justice is currently presiding, my guess is he could, and would, expedite any appeal to the full Supreme Court.
I don;t think he even has to do that. I think he can just say yes or no when it comes to executive privilege being extended to Bolton.
He does have connections in that direction, but I suspect he also has the authority to order compliance. In any case, the correct path would be to tell the House managers to try again, investigate before they vote to impeach, and put the witnesses they want in their second (or perhaps third, or fourth) impeachment.
Linda Graham said the House brought this mess to the Senate and is forcing them to decide to eliminate executive privilege or honor it. He’d vote to honor exec privilege because the House didn’t do their job and go through the courts.