No, it isn't a bill, but an official vote is still part of the proceedings in both chambers. It is only on a vote of Impeachment (similar to a grand jury decision) that the baton is then passed to the Senate for a vote of Conviction.

Remember, this did happen to President Clinton. He was impeached by the House. He just fell short of conviction by the slimmest of margins because the Democrats voted party-line.

I have read the anti-federalist papers (many years ago), and they are indeed inspiring, especially when the 'federalist' papers are read in parallel. while I am inspired, the result is the same. They were the politicians of their day. The results of their ideas has been annointed as saintly by generations of politicians and historians. The bottom line, however, is different. The anti-federalists were as naiive (or complicit) as the federalists were statist. The primary reason that individual liberty and all the benefits that come from it have lasted at all was the later addition of the Bill of Rights. Without the Bill of Rights, the constitution primarily transfers power from states to central government. It does not include the bold statements of the Declaration of Independence which so profoundly describes individual rights and their source. If you read it, you will see the fear of European powers in the background. The anti-federalists succummed to those fears and surrendered power to the central state even while trying to set up a framework to bond the states together in fear of European monarchs. They did restrict the power of the president somewhat, most not wanting another monarch. Living in a new near empty continent, a frontier, they failed to prepare for the eventuality that the central government, if not overtly limited, would be subject to the same human nature of the governments of Europe. Instead they recognized that in the states and forbade them from reorganizing. The language of freedom from the Declaration was omitted. The whole constitution appears to be a set of rules for bureaucracy, but includes little to limit the central government overtly. Only later with the Bill of Rights were limits stated, albeit recently those are circumvented or ignored for 'national security' or other convenience. Some of the federalists knew what they were doing, having visions of grandeur of empire.
Yes, your state of mind does affect how the document is understood. We do not stand here, a weak group of states, the only republic in the world standing against powerful monarchs in Europe, existing in a wilderness needing every man to work hard for our very survival. We see a dictatorial central power of elitist looters that bribes the less capable and the less industrious among us to steal from those who willingly strive for self reliance in a modern world of many conveniences. These statist looters steal away the unalienable individual rights as the statist monarch did in the Declaration of Independence. I see two documents (the Articles and the Constitution) that made this abomination possible. In retrospect, the Constitution appears a greater threat to individual liberty.