My only thought is playing exactly the same rhythm for each song is will become boring for you in the long run and the band will get lazy!
You don't need to be complex, but look for other ways to accent the beat, for example playing a different 'connecting' note as that last quaver to signal each chord change, or changing the dynamics so you play 'straight eights' but the first note is struck harder so it's louder.
If the songs are covers, have you looked them up on a tab site? There are usually some straightforward fills or riffs that help round out the bass in most popular songs and it can be really satisfying to nail them.
Funnily enough I'm listening to 'Dancing in the Dark' as I type this - all straight 8th notes on the root, except (according to Ultimate Guitar) one single 'leading' note in the bridge. A good example of what I mean by a 'connecting' note. But beware too much of that and you'll end up playing walking basslines:
[Bridge]
G|----------------|----------------|----------------|----------------|
D|----------------|----------------|2-2-2-2-2-2-2-2-|4-4-4-4-4-4-4---|
A|----------------|2-2-2-2-2-2-2-2-|----------------|--------------2-|
E|4-4-4-4-4-4-4-4-|----------------|----------------|----------------|
G|----------------|----------------|----------------|----------------|
D|----------------|----------------|2-2-2-2-2-2-2-2-|4-4-4-4-4-4-4-4-|
A|----------------|2-2-2-2-2-2-2-2-|----------------|----------------|
E|4-4-4-4-4-4-4-4-|----------------|----------------|----------------|