First, I understand what modes are and generally how they are constructed (starting a C-scale, for example, then starting the scale from one ascending hole tone so you end up with different tonalities). What I don't understand is how and where to use them.
Do you play jazz? I think when talking about modes usually people have jazz and improvisation in mind, but modes are there in every song. The difference is perhaps that in jazz the players change modes within a song continuously, while a non-jazz song probably stays in the same mode throughout. Jazzists would not probably say you're using modes if you don't change them within a song. And yet, if you were a composer of songs, and purposefully changed mode between songs, to exploit their different moods, then you would definitely be using modes.
I personally think there's an interesting middle ground that can help understand the compositional usefulness of modes, which would be to change modes across sections of a song. That is, not every chord, and not first fixing chords and then choosing modes that fit on those chords, but instead compose a section based on one mode, and choose chords that fit such mode. This is a lot easier from a mental point of view, as you are not overwhelmed by possible choices: once you are set on a mode in a section, you know exactly which 7 triads chords you can use, and all their possible extensions.
This approach won't teach you practical jazz improvisation. It will help only on learning the mood or meaning of a mode. It however also makes it clear that harmony is at band's level: it is the whole band which plays a chord AND a mode. Saying what chord the band is playing is not enough if each player then thinks they can play whatever mode they want as long as it's compatible with the chord, it has to be the same mode for all (well, nothing in music is against the law! but if they play different modes then there's a risk the piece will end up sounding all chromatic/dodecaphonic).
This simple consideration is to come back to the bassist's options with modes. If you are in a jazz context, maybe the players take turns in soloing. If you don't agree beforehand which mode the soloist will use over each chord, all others should stick to the notes of the chords for safety. If they start embellishing, they risk mismatching the soloist's mode. Otherwise, agree beforehand and you know how to match. As a bass player, there is a chance you won't solo or your solos will be shorter or less frequent. That's not a problem, the problem is the somewhat common tendency of keyboardists and guitarists to think they need to embellish during your solo, which they otherwise think it's too thin: for this reason I'd recommend to let them know your chosen modes in advance.
This is what I had in mind, thanks for being the only one to point it out. As a fundamentally non-improviser, I could sense how everyone else in the thread was focused on "modes as chord-scales" for improvisation, but it's not the only way.I've said this before on TB, but I think there's often a confusion between "modes as [something like] keys" and "modes as chord-scales."