"It is a sad day for America to see Senator McConnell humiliate the Chief Justice of the United States into presiding over a vote which rejected our nation's judicial NORMS, precedents and institutions which uphold the Constitution and the rule of law," Pelosi said Saturday on Twitter.

Contrary to claims by Trump and some Republican allies, House Democrats did seek testimony from Bolton, but he declined to appear for his deposition under White House orders.

Former Trump adviser Bolton threatened to sue if subpoenaed to testify in impeachment probe: committee (7 Nov 2019)

The House did not issue a subpoena because, Democrats said, it would only prolong the process.

Schumer, Amd. 1296

Mr. SCHUMER proposed an amendment to the resolution  S.Res. 488
[...]
Notwithstanding any other provision of this resolution, pursuant to rules V and VI of the Rules of Procedure and Practice in the Senate When Sitting on Impeachment Trials, the Chief Justice of the United States, through the  Secretary of the Senate, shall issue a subpoena for the taking of testimony of John Robert Bolton, and the Sergeant at Arms is authorized to utilize the services of the Deputy Sergeant at Arms or any other employee of the Senate in serving the subpoena authorized to be issued by this section.

Mr. SCHUMER proposed an amendment to the resolution  S.Res. 488
[...]
Notwithstanding any other provision of this resolution, pursuant to rules V and VI of the Rules of Procedure and Practice in the Senate When Sitting on Impeachment Trials, the Chief Justice of the United States, through the Secretary of the Senate, shall issue a subpoena for the taking of testimony on oral deposition and subsequent testimony before the Senate of John Robert Bolton, and the Sergeant at Arms is authorized to utilize the services of the Deputy Sergeant at Arms or any other employee of the Senate in serving the subpoena authorized to be issued by this paragraph.

Mr. VAN HOLLEN proposed an amendment to the resolution S.Res. 488, to provide for related procedures
[...]
Notwithstanding any other provision of this  resolution, the Presiding Officer shall issue a subpoena for any witness or any document that a  Senator or a party moves to subpoena if the Presiding Officer determines that the witness or document is likely to have probative evidence relevant to either article of impeachment before the Senate, and, consistent with the authority of the Presiding Officer to rule on all questions of evidence, shall rule on any assertion of privilege.