The bassist is the time keeper for the band and is a crucial part of the rhythm section as it underpins everything. Bassist and drummer must lock in together to form the foundation of the ensemble.
A lot depends on the style of music: for Swing and a lot of Jazz, bass is characterised by a walking bass line - 4 x quarter notes to the bar. In other styles such as Funk, it is about the groove.
Sometimes a bassist is required to read a part - a specific line; and at other times, the bassist will create their own lines based upon the chord chart provided. An effective bassist in a big band must be both a good reader as well as improviser of many styles. Needless to say, their sense of time must also be impeccable.