There is no Constitutional amendment dictating how a secession is to be executed.

In that vacuum, you don't get to make up your own rules.

To secede, all parties would have to get together and make that decision, make up a bill and get it passed through congress and singed by the president.

You don't get to mount an insurrection and then call it a secession.
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Article I, Section 8, Clauses 11, 12, 13, 14: War; Military

To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
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Supremacy Clause follows the lead of Article XIII of the Articles of Confederation, which provided that "[e]very state shall abide by the determinations of the united states in congress assembled, on all questions which by this confederation are submitted to them."
http://www.heritage.org/constitution/#!/articles/6/essays/133/supremacy-clause
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Then, by no means was secession unanimous amongst the people of the Southern States.

By bypassing congress and keeping it within the states, those that opposed secession were denied their rights to to gain support and join with others from other states who felt the same way.

The sudden departure of seven states from the Union and the establishment of a southern nation gives an impression of a unanimous popular movement following Lincoln's election. In fact, however, opposition to immediate secession was notable in most of the seceding states, and became quite potent as one proceeded northward towards the border and upper South region. The elections of delegates to secession conventions were close in a number of deep South states, belying the greater majorities for secession at the conventions themselves. In Georgia, for example, the votes for secessionist delegates constituted at best a bare majority and may well have actually been outweighed by voters opposing immediate secession. In Alabama and Louisiana, the vote was also very close. Opposition to immediate secession was not the same as devotion to the Union, but it suggested that some kind of compromise could return most, if not all, of the seceding states back to the Union.
In the upper South, where slavery was less prominent and association with the North more pervasive, opposition to immediate secession was even stronger. States like Virginia, Tennessee, and Arkansas took a wait-and-see attitude, sometimes calling for a convention, sometimes rejecting demands. Even where conventions were called, pro-Union delegates predominated. Thus, Virginians held an election for a convention on February 4, but the secessionists were outpolled about two to one. A few days later, Tennessee voters went even further and rejected a move to call a convention. Thus, after the secession of Texas in the beginning of February 1861, secessionist momentum ran into a wall of resistance. Eight slaveholding states remained in the Union. How to keep them there, especially by avoiding the outbreak of actual fighting, was a matter of considerable urgency to unionists in the days following Lincoln's election. Not surprisingly, the upper South was the main source of compromise initiatives intended to provide for an honorable and peaceable restoration of the Union.
http://www.tulane.edu/~sumter/Background/BackgroundUpperSouth.html