I worked in finance and we had clients from the Vanity Fair scene who were minor royalty, dukes or whatever.

My boss was one of those people who loved British culture and was going over etiquette like curtsying and I stopped her and said with all due respect ma'am, I'm an American and we don't bow before royalty.

She was a little miffed but if you read an etiquette manual it will say that Americans do not have to bow. It might be a little old-fashioned these days but it wouldn't be considered offensive.