In terms of British politics, the American Revolution aligned more with the Whigs than with the Tories. That aligns them with constitutional monarchy and the "bourgeoisie" over monarchical absolutism and the nobility. However, they were also republican in nature - they opposed monarchism altogether.

By modern standards, we might consider them conservative in a way. They were led be colonial elites. They were for republicanism, but not democracy. But by the standards of the time, they were Enlightened liberals against monarchical conservatives. And the revolutionary generation of American elites didn't necessarily see eye to eye on everything. They would later split into "conservative" Hamiltonians and "liberal" Jeffersonians. But again that doesn't translate easily into our modern spectrum. The Hamiltonians were for big government while the Jeffersonians were for small government - but it was a form of elitism vs. a form of democracy. The federalism and anti-federalism, respectively, of these two factions became an enduring trend in American politics. But politics changed over time. Now we think of liberal Democrats being for big government and conservative Republicans being for small government.

So, that is kind of a simplistic analysis, but I think it helps to prove my point. By the standards of the time, they were not conservatives. Politics has changed a lot since then, and some modern conservatives like to trace their political heritage to the American Revolution. The implication is that modern liberals are "less American". My opinion: don't buy into that crap. Both are unique to the American political spectrum and come out of the American Revolution and its aftermath, and have changed over time. Also, it doesn't make any sense to call the American Revolution "conservative" in a modern sense as opposed to the modern "left wing", the labor movement, environmental movement, civil rights, women's rights, and so on - none of the modern movements for social change existed yet.

Where have you heard that? From what I know, in the context of the time, conservatives where usually aligned with the church and the monarchy, while liberals held Enlightenment ideals about government.

Edmund Burke would certainly argue that the American Revolution was truly a conservative movement. He believed that all people possess a desire to maintain order without severe and drastic change. In his mind, when a government moves against that ideal, revolution and unrest is warranted and justified. So when the British government began to impose sanctions and new taxes on the colonists, they were changing the status quo of the colonies in a harmful way. In his mind, this gave the colonists right to revolt. They were overthrowing their government to prevent change, not to cause it.

This was in stark contrast to his views on the French Revolution, which he viewed as completely unjust. That was an example of a radical movement in his mind.

Source: Edmund Burke: Reflections on the Revolution in France