Reluctantly, due to Bush's rejection of the courts, Congress is compelled to use this remedy.

they would prefer to use the courts of course but Bush insists it can not be done.

McGrain conceded that the conviction was valid, he questioned the Congress' power to punish as opposed to compel via a contempt conviction.

But McGrain basically precludes the line of inquiry you propose and is not at all what Bush's objection is. To wit, McGrain states:

We come now to the question whether it sufficiently appears that the purpose for which the witness' testimony was sought was to obtain information in aid of the legislative function. The court below answered the question in the negative and put its decision largely on this ground, as is shown by the following excerpts from its opinion (299 F. 638-640):

'It will be noted that in the second resolution the Senate has expressly avowed that the investigation is in aid of other action than legislation. Its purpose is to 'obtain information necessary as a basis for such legislative and other action as the Senate may deem necessary and proper.' This indicates that the Senate is contemplating the taking of action other than legislative, as the outcome of the investigation, at least the possibility of so doing. The extreme personal cast of the original resolutions; the spirit of hostility towards the then Attorney General which they breathe; that it was not avowed that legislative action was had in view until after the action of the Senate had been challenged; and that the avowal then was coupled with an avowal that other action was had in view-are calculated to create the impression that the idea of legislative action being in contemplation was an afterthought. ...
'That the Senate has in contemplation the possibility of taking action other than legislation as an outcome of the investigation, as thus expressly avowed, would seem [273 U.S. 135, 177]   of itself to invalidate the entire proceeding. But, whether so or not, the Senate's action is invalid and absolutely void, in that, in ordering and conducting the investigation, it is exercising the judicial function, and power to exercise that function, in such a case as we have here, has not been conferred upon it expressly or by fair implication. What it is proposing to do is to determine the guilt of the Attorney General of the shortcomings and wrongdoings set forth in the resolutions. It is 'to hear, adjudge, and condemn.' It so doing it is exercising the judicial function. ...
'What the Senate is engaged in doing is not investigating the Attorney General's office; it is investigating the former Attorney General. What it has done is to put him on trial before it. In so doing it is exercising the judicial function. This it has no power to do.'
We are of opinion that the court's ruling on this question was wrong, and that it sufficiently appears, when the proceedings are rightly interpreted, that the object of the investigation and of the effort to secure the witness' testimony was to obtain information for legislative purposes.

It is quite true that the resolution directing the investigation does not in terms avow that it is intended to be in aid of legislation; but it does show that the subject to be investigated was the administration of the Department of Justice-whether its functions were being properly discharged or were being neglected or misdirected, and particularly whether the Attorney General and his assistants were performing or neglecting their duties in respect of the institution and prosecution of proceedings to punish crimes and enforce appropriate remedies against the wrongdoers; specific instances of alleged neglect being recited. Plainly the subject was one on which legislation could be had and would be materially aided by the information which the investigation was calculated to elicit. [273 U.S. 135, 178]   This becomes manifest when it is reflected that the functions of the Department of Justice, the powers and duties of the Attorney General, and the duties of his assistants are all subject to regulation by congressional legislation, and that the department is maintained and its activities are carried on under such appropriations as in the judgment of Congress are needed from year to year.