To be sure, drummers are not essential. Consider the Nat King Cole Trio or Oscar Peterson's first trio with Herb Ellis on guitar instead of a drummer. Or even a modern example: Lisa Lindsley, who cut a remarkable album with just a pianist and bassist.
The lack of a hard requirement for a drummer extends to other genres too. Most of blues vocalist Alberta Hunter's later live performances were with just a pianist and bassist.
Why am I harping on this? It's to give you pause to consider that as a drummer you need to bring something to the table if you do not want to get replaced by a backing track or guitarist. One way to prove your value is to integrate into the ensemble and support the music instead of just providing time and a beat. And the way to do that is to make the bassist your best friend (which should be the case anyway.)
Let's check out a clip where the bassist truly adds to the music sans drummer:
Here is a famous clip where it's just a bassist and drummer. I am not advocating playing flash and novelty, but the interaction between the two and the fact that the foundation of the rhythm section pulled this off shows what a locked in bassist and drummer can do. The drummer here is the great Ray Bauduc:
Examples of bass and drums abound, but here is one album that I particularly like: Percussion And Bass, if for no other reason that it features one of my favorite drummers and personal inspirations - Papa Jo Jones - and does epitomize the partnership between bassists and drummers.
Another album worth checking out is The Supreme Bassists and Drummers, which is heavily slanted towards Charles Mingus and Dannie Richmond and Art Blakey paired with various bassists. It also has some swing represented by Gene Krupa and Buddy Rich paired with various bassists. Don't let the electric bass on the album cover fool you - all of the bass is played on a double bass by some real masters.
I could go on and on. For example, the albums mentioned in My Personal Rushmore are filled with examples, and are especially rich in recordings by the All-American Rhythm Section comprised of Basie on piano, Freddie Green on guitar, Walter Page on bass and Papa Jo Jones on drums. Or the 1959 albums that changed jazz, which included Paul Chambers paired with Jimmy Cobb, Charles Mingus paired with Dannie Richmond, Eugene Wright paired with Joe Morello, and Charlie Haden paired with Billy Higgins.
Another way to form that important partnership is to see things from the bassist's perspective. This masterclass conducted by the great Ray Brown will reveal that perspective.
I'll end with two clips. First is a clip from Diana Krall - Live in Paris that illustrates the essence of this post. Check out the way Jeff Hamilton on drums is locked into John Clayton on bass, and how both of them beautifully support Diana and Anthony Wilson. The second clip is Ray Brown, Jeff Hamilton on drums and Gene Harris (of Three Sounds fame) on piano.
Ray Brown, Jeff Hamilton and Gene Harris