Final answer:
George H.W. Bush spoke at various Republican National Conventions, particularly in 1988 when he was the party's nominee for president. The provided materials do not give exact dates of his convention speeches. Conventions typically correspond with the presidential election cycle every four years.
Step-by-step explanation:
George H.W. Bush spoke at the convention when he was a key figure in the Republican Party. He was the running mate of Ronald Reagan in 1980 and became Vice President after they won the election. His prominent role in the party after serving as Reagan's Vice President meant he spoke at multiple conventions, but the question seems to be focused on his time around the presidency. In the 1988 convention, he was the Republican nominee for president following Reagan's two terms. Unfortunately, the provided text does not specify the exact dates of his speeches at the conventions.
However, conventions typically occur every four years preceding a presidential election, aligning with the election cycle. As president, George H.W. Bush faced challenges such as the Iran-Contra Affair, raised taxes contrary to his earlier pledge, and led military operations such as Desert Shield and Desert Storm, topics that would be pertinent in his speeches and public appearances while in office.