For me, it depends on several factors, in this order:
- Is the bass comfortable to play or capable of being properly set up. Above all you need an instrument that fits your body, hands and can be properly set up. The electrics of a musical instrument are fairly basic and simply provide a signal to the amp. As long as it isn't buzzing, humming or cutting in and out, there is no need to upgrade just yet.
- What purpose is the amp being used for? The biggest limiting factor in the sound of an amplified instrument is the speaker. A practice combo amp (low power, small speaker) usually has a headphone output and some even have aux input so you can play along to outside music. The headphone will sound tons better than the dinky speaker. If the amp is solely for practice, I wouldn't bother upgrading just yet....if you are in the student phase.
- If your combo amp is filling multiple roles (practice, rehearsal, performance) you will definitely want an amp with tone shaping options but, most of all, you'll need something will good speakers. The best bass with the best electrics with the best amp possible will sound like garbage when played through a garbage quality speaker.
Of course this is only my humble opinion. Good luck!