A book I'd recommend to you is called I do! Courtship, Love and Marriage on the American Frontier: A glimpse at America’s romantic past through photographs, diaries and journals (1715-1915) by Cathy Luchetti. Long title, but an amazing book about America's more romantic history. It includes the engagement traditions of different cultures and races from whites to native americans to asian-americans to african-americans and so on. Very interesting.

However, I'm not sure I'll be able to answer your question without a little more clarification. The "American experience" is still a little broad. America is a country made up of immigrants who brought their courting/engagement customs with them and intertwined them with others over the years. Are you asking about the white population, particularly those of British decent or another culture?