Your question contains two assumptions that need to be corrected before we get started, and those two assumptions contain your answer, I think. :)

First, let's explain that the list of constitutional rights, the Bill of Rights is a separate document from the Constitution itself. At the time the Constitution was drafted and put to the states for consideration, there were two significant political factions in the United States: the Federalists and the Anti-Federalists. The Federalists believed in a strong central government and discouraged democracy. They believed that a true democracy would be vulnerable to populism and mob rule. Therefore, they wanted a strong state, more like the ones in Europe, but with a republic instead of a monarchy. These were men like Alexander Hamilton, John Adams, and George Washington.

The Anti-Federalists took the opposite tack. They believed that personal liberty and personal rights should be paramount, and that state and local governments should be strong, not the federal government. They believed the problem with European governments wasn't that they were monarchies, but that they had strong central governments with large armies and bureaucracies. These were men like George Mason and Thomas Jefferson.

When the Constitution was proposed, it was opposed by Anti-Federalists concerned that the government it created was too similar to European-style despotism as it existed at the end of the 18th century. Anti-Federalist sentiment was so strong that it threatened the implementation of the Constitution. Without modifications, not enough states would approve the Constitution, and it would not become law. This is why the Bill of Rights was created; it was a compromise intended to ensure passage of the Constitution. The Constitution came first, and the Bill of Rights came later, and so the two should be considered separate items with separate influences and separate origins.

Now, let's talk about the second assumption: that "corruption" means the same thing today as it did in the 18th century.

Let's consider the Federalists, who won the first three U.S. Presidential elections and held control of Congress for much of that period. The Federalists (and it'd be inappropriate to call them a political party, so let's call them a movement) came from the belief that disinterested government was the best government. The ideal politician, they believed, was an elite individual educated to understand the issues and able to consider each one in a detached way. This meant political representation from an aristocracy of educated, landed people whose income was assured via rents, inheritance or other, similar means. Because these people didn't have to worry about earning money, they wouldn't have to worry about their financial affairs affecting their votes. They would be able to consider matters dispassionately and render impartial laws. The new government wouldn't even have to pay salaries to politicians and office-holders because they would be expected to support themselves through their existing income.

The problem with this approach, of course, is that by assigning representation to a small aristocracy, you create a very unrepresentative government. Aristocrats do not have the same wants and desires as someone who works for a living, and they move in a select circle. They're prone (as Hamilton's dealings with the Bank of the United States showed) to making deals within that select circle. Because they believe that non-aristocrats are subject to improper influences, they're prone to awarding contracts and making arrangements only with other aristocrats. Because of their strong-held beliefs in impartiality and neutrality, the early Federalists corrupted the system toward other Federalists.

The problems this created were quickly apparent. After the French Revolution began to disrupt European commerce and industry, America profited enormously. Americans, particularly those in the shipbuilding and trading fields, reaped huge profits, and the new nation's population boomed through immigration and new births. Thus, the aristocratic sliver of the United States shrank, proportionally, and the idea of an elite republic started to falter in Washington's second term.

The Republicans, who succeeded the mantle of the Anti-Federalists, desired a representative republic with delegates drawn from the "middling sort" of merchants, manufacturers and tradespeople. This was a toxic idea to the Federalists, particularly after the French Revolution spawned the Great Terror and seemed to show the critical danger that Republican ideals could bring.

As we know, however, Republican ideals won out. Federalist moves like the Alien and Sedition Acts backfired tremendously, and Thomas Jefferson swept into office in 1800 with a huge Republican majority in Congress.

The American government had, in the eyes of Federalists, been completely "corrupted". Now, politicians would be vulnerable to outside influence because they didn't have the ability to support themselves without working. Even worse, they would actually listen to their constituents and instead of governing impartially and disinterestly, they would be prone to the ebb and flow of "popular opinion," which became a term for the first time. Instead of being nominated for office as a prominent member of the community, politicians would have to campaign for office, pledging and offering favors.

This period of American history is incredibly fascinating; it's like a boiling pot. I really suggest picking up some of Gordon Wood's books if you're interested in the topic. Empire of Liberty and The Creation of the American Republic are a great pairing if you're starting out. Don't be intimidated by their size. They read easily, and they're wonderful.