Well Jazz is the last genre not fucked over on radio nowadays. So my recommendation is keep going back for more.
From My iTunes Library, artists with the Jazz genre tag:
-Artie Shaw
-Benny Goodman
-Bessie Smith
-Billie Holiday
-Bud Powell
-Cassandra Wilson
-Cecil Taylor
-Charles Mingus
-Charlie Parker
-Chet Baker
-Chick Webb
-Coleman Hawkins
-Count Basie
-The Crusaders (or Jazz Crusaders)
-Dave Brubeck
-Dexter Gordon
-Dizzy Gillespie
-Django Reinhardt
-Duke Ellington
-Ella Fitzgerald
-Ethel Waters
-Fletcher Henderson
-Frankie Trumbuaer
-George Krupa
-Glenn Miller
-Grover Washington Jr.
-Herbie Hancock
-Horace Silver
-J.J. Johnson
-Jaco Pastorius (not really jazz, strictly)
-Jelly Roll morton
-John Coltrane
-Julie London
-Louis Armstrong
-Matt Roberts Group
-Miles Davis
-Quincy Jones
-The Seatbelts (the japanese jazz band behind Cowboy Bebop)
-Thelonious Monk
-Tommy Dorsey
-Weather Report (jazz FUSION!!!)
-Wynton Marsalis
I have more but it's not categorized. You can't go wrong with that list. Plenty of it isn't jazz of the nature you described, but restricting yourself to the piano-drum-upright bass combo in such a vast genre is like restricting yourself to 80s arena rock when you're trying to get into metal.
tl;dr:
Charles Mingus, Count Basie, Jazz Crusaders, Dave Brubeck, Dizzy Gillespie, Duke Ellington, Glenn Miller, Herbie Hancock, J.J. Johnson, John Coltrane, Matt Roberts Group (LA local band which have become one of my all time favorites), Miles Davis, Quincy Jones, Thelonious Monk, Wynton Marsalis. And branch out to the rest later.