As stated before, your bassist can use a regular fretted bass. Alternately, your bassist can play a fretless bass. Like other fretless instruments, the fretless bass can tune-up notes while playing.
Bill Wyman, the Rolling Stones’ bass player, made his own fretless bass. Along with Richard’s open tunings, Wyman’s fretless bass was essential in creating the Stones’ late sixties/early seventies sound.
According to Wyman, his first bass was a cheap instrument. He had someone cut down the body, and Wyman removed the paint. Then, he sanded it and beveled the edges. Also, the bass had worn frets, so he pulled them.
Wyman describes the sound he got, “…when I pulled ‘em out, it suddenly sounded really good! [Laughs.] …but you had to be dead on to be in tune. Anyway, I never put frets back in, and I think it was the first fretless electric ever. I used it on every Stones album and many of the singles up to 1975” (34).
Wyman also says that he used the gaps where the frets used to be as a guide for tuning. However, it is also likely that he subconsciously fine-tuned the pitch, allowing the guitars and flexible pitch instruments to sound even better.
Similarly, Geoff Emerik, the Beatles recording engineer, said of Paul McCartney, “I’ve actually seen Paul’s fingers bleed from pulling out the notes, getting the notes to speak properly” (88).
This just goes to show the talent that these players had. It also shows the lengths they went to in search of a better sound or to be better in tune. If you want to jam like a rock star, you need the same level of commitment to your gear and your craft.