Was the phrase "British Colonial America" used during that period? (obviously ignoring French, Spanish, and Native possessions)
It would seem that, following the rule to "Use their conventions not ours", the correct form for the period preceding the Revolution would in general be Town/County/Colony. There are no larger political entities.
For clarity's sake (and in the absence of contemporaneous documents), I suggest adding the geographically correct "New World" between 1492 and approximately 1560, and "America" for the period of 1560 (around the time that the term became common) to the Revolution.
For American Patriots, the English colonies become "The United States of America" in 1776. For Loyalists they remain English until the Treaty of Paris in 1783.