I believe that Bache believes Americans should support the French Revolution despite the bloodshed taking place in France because he viewed it as a part of revolution by mankind for liberty.
He thought that the Revolution was a perfect proof of who really is in power - the people are those who choose their leaders, and the government is powerless if they decide to band together and fight for their rights. Americans supporting this Revolution is important because of their own Revolution against their tormentors, Britain.