Why do you think colonists believed they were entitled to the rights guaranteed by the Magna Carta and the English Bill of Rights?
They considered themselves to be Englishmen.
Prior to the Declaration of Independence in 1776, the people of the 13 colonies considered themselves Englishmen first and Americans 2nd. For the 10 years preceding the war, they continuously pushed for a seat in parliament as was the right of all Englishmen. They were always denied. The properly argued, even if unsuccessfully, that it was their right as Englishmen dating back to the Magna Carta to be afforded that right.