Everyone gets constitutional protection. Read the Bill of Rights. Look for the word "citizen". You won't find it. The constituion speaks of "persons" and "the people". The only people who are not entitled to the full protection of the constitution are US soldiers and sailors serving in time of war. Pay particular attention to the fifth and sixth ammendements.
The constitution says quite plainly that Bin Laden, if he comes to trial, is to be tried by a jury of the state of New York.
Amendment V
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
Amendment VI
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.
Trials for the Enemy by the New York Post.