Were that the case, he would have publicly criticized the Virginia convention for ratifying the unamended Constitution in July 1788.
What was his response to the ratification? He wrote a private letter, which your source quoted, to James Madison saying: "I hope, therefore, a bill of rights will be formed to guard the people against the federal government" and he did not write a public "I am dead against this Constitution!" remonstrance.
He "hoped" that the amendments would be made. That's not a particularly aggressive stance, but it is a wisely considered one.
Since you don't like me doing the copy/paste thing... Copy the above link and read his letter to Madison from 1787. It wasn't just the failure to include a BoR, but lifetime Presidency and other matters as well.
Several of his letters after this contain further disapprobation.
Hardly supportive as you've suggested.