Based on their origins, the order from oldest to newest is:
Blues
New Orleans Jazz
Swing
Bebop
Chronology of Music
Blues began in the 1860s in the Deep South.
New Orleans Jazz started in the 1890s.
Swing started in the 1930s
Bebop started in the 1940s.
What we can conclude therefore, is that Blues came first and was followed by New Orleans Jazz. Swing then followed after which came Bebop.
In conclusion, Blues have been around a long time.