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As a musician who plays the drums, your partner in rhythm in the band is the bass player. Together you lay the foundation for the songs you play. Here are some thoughts and examples on relating to your bass player in different musical situations.
Start by thinking about the musical genres and styles that you play. Your roles playing latin jazz will be different than your roles playing death metal, for example. Sometimes the two of you need to be rhythmically locked in together. Other times, one of you holds down the rhythm while the other flows or plays melodically. One of you may need to lay back or play ahead against the other to provide the proper feel.
I recommend you analyze your favorite songs to pay attention to what the rhythm section is doing.  Let’s listen to a handful of songs to see what the bass and drums do to make those songs work. Pay particular attention to the dynamics and feel of each instrument.
Can’t Always Get What You Want” The Rolling Stones
Drums: Charlie Watts, Bass: Bill Wyman

The bass and drums pretty much line up here.

“Taxman”  The Beatles
Drums: Ringo Starr, Bass: Paul McCartney

Here the bass and drums line up playing the same rhythm, except the bass line doesn’t play on beat 4. This plays well against what the guitar is playing and highlights the snare hit on the 4.

“My Favorite Things” John Coltrane 
Drums: Elvin Jones, Bass: Steve Davis

This one is a jazz standard. The bass is holding down the rhythm, accentuating the downbeat, while the drums are flowing triplets.

“Another One Bites the Dust” Queen 
Drums: Roger Taylor, Bass: John Deacon

The bass here plays the main riff while the drums hold it down.

“Around the World” Red Hot Chili Peppers
Drums: Chad Smith, Bass: Flea

The bass line is playing melodically while the drums hold down a 16th note part.

“Fire” Jimi Hendrix
Drums: Mitch Mitchell, Bass: Noel Redding

This is an example of the bass, and guitar, leaving space for drums to get expressive.
Of course, music is subjective. There are multiple ways these songs could have been approached, but they are good examples of how to work within the rhythm section. After analyzing the music, get with a bass player and practice together. If you are in a band, you can have sectional rehearsals with just you and the bass player to work things out.