You wouldn't be the first person to describe Bolero as being a cross between Rumba and Waltz, although in recent years, it has become much more Rumba, with a lot less Waltz.
Being a Latin dance, Bolero's footwork is mostly ball-flat. True, there is some rise & fall, but it's mostly body rise, not foot rise. And there's no driving or swinging action, so heel steps do not apply.
Is it an "American invention?" Not exactly. The style as it is currently danced (as shown in the Bolero videos on this website) was probably developed in American ballrooms/nightclubs/dance studios, but historically speaking, there's nothing American about Bolero.
From a historical standpoint, Bolero is simply a type of Rumba. It is the slowest of all of the various Rumba forms, and so if you think about it, the International style of Rumba should technically also be classified as a Bolero.
Almost every one of the ballroom dances is a bastardization of some authentic form of dance, and Rumba is certainly no exception. The American style "Bolero" and the International style "Rumba" are both very loosely based on the Bolero form of Rumba that finds its roots in Africa and Cuba, but you wouldn't know it if you were to see the modern ballroom versions danced next to the originals. They are far more similar to each other than they are to the dance form on which they are based.
Incidentally, I've read somewhere that the American style Rumba is based on "Son Rumba", a faster version of Afro-Cuban Rumba. But I suspect that's mostly myth. I think American Rumba was basically an Arthur Murray invention, which began as little more than a Box step. It then developed concurrently with American Bolero and Int'l Rumba throughout the latter half of the twentieth century. Now all three dances share the large majority of their syllabus patterns in common, and the basic styles of movement are little more than different shades of the same basic technique.
Regards,
Jonathan
