Is George W. Bush the first President to issue signing statements?

NO. Several sources trace “signing statements” back to James Monroe. Interesting early statements that include discussions about presidential doubt about legislation and the issue of how the president should proceed are found from Andrew Jackson, John Tyler, James K. Polk, and Ulysses Grant. A brief overview can be found in the ABA Task Force cited below. Monroe’s messages did not look like what are today considered “signing statement.” Rather he informed Congress in a message January 17, 1822, that he had resolved what he saw as a confusion in the law in a way that the thought was consistent with his constitutional authority.

Even more forcefully, Monroe sent another message dated April 6, 1822, (that refers to his January 17, 1822 message as having “imperfectly explained” his concerns) stating “If the right of the President to fill these original vacancies by the selection of officers from any branch of the whole military establishment was denied, he would be compelled to place in them officers of the same grade whose corps had been reduced, and they with them. The effect, therefore, of the law as to those appointments would be to legislate into office men who had been already legislated out of office, taking from the President all agency in their appointment. Such a construction would not only be subversive of the obvious principles of the Constitution, but utterly inconsistent with the spirit of the law itself, since it would provide offices for a particular grade, and fix every member of that grade in those offices, at a time when every other grade was reduced, and among them generals and other officers of the highest merit. It would also defeat every object of selection, since colonels of infantry would be placed at the head of regiments of artillery, a service in which they might have had no experience, and for which they might in consequence be unqualified.”

On May 30, 1830, Andrew Jackson wrote a message to the House stating his understanding of the limits of an appropriation: “the phraseology of the section which appropriates the sum of $8,000 for the road from Detroit to Chicago may be construed to authorize the application of the appropriation for the continuance of the road beyond the limits of the Territory of Michigan, I desire to be understood as having approved this bill with the understanding that the road authorized by this section is not to be extended beyond the limits of the said Territory.” His reference to how he may "construe" the language of the act has been echoed often in the modern era.

Tyler, issued (March 23, 1842) a prototypical “reluctant” signing statement, in which he signs a piece of legislation concerning legislative apportionment while announcing, for the record, that he thinks it is unconstitutional.

Polk in August 1848 similarly warned that while he was signing legislation that established a government in the Oregon territory prohibiting slavery, that he would not have signed similar legislation that involved New Mexico and California south of the “Missouri Compromise Line”.