Generally, you will find that effects are not a desirable sound for most of your bass-playing needs. This is because most effects tend to distort the clarity of the bass sound. This goes for reverb, delays, flanging, chorusing, distortion, fuzz, and most other effects.
However, there are certain times, when effects are the appropriate course of action. Musical taste is the key here, and it is a decision that you or someone else in your group should make. Generally, the appropriate time to use an effect is when the bass is featured or in solo mode.
A good example of this is East River Drive, by Stanley Clark. While the entire album is a solo feature of Stanley, on the song titled East River Drive, there is a section where the bass is playing a solo.
Stanley is using his Alembic bass with light gauge strings, and the effect he is using is a heavy flanging effect. This effect often diminishes the clarity of the bottom end of a bass sound, since it is essentially a shifting delay effect, usually 10ms to about 50ms.
But since he is playing a lead part, the effect on the bottom end is insignificant, since he is playing in the upper ranges of the bass.
I did a recording of a Jazz bass playing the melody against the backdrop of a vocalist. The bass would play the phrase first, then the vocalist would echo this part.
For the bass, I selected a large bright reverb room. This effect worked nicely since there was plenty of open space for the bass at these times.
Another example is Chris Squire on the Relayer album, with the song called Sound Chaser. In the middle of this 9-minute song, the bass is playing softly with an electric guitar, and strings in the background.
The bass sound has a lot of dark-colored reverb. This would normally be a no-no, but it is used tastefully and gives this segment a wonderful aura.
Another example of tastefully featuring a bass with effects is Marcus Miller on the Spellbound album, first track. Towards the end of the song, there are three notes played as a snap on the G string (C-D-C) between two piano fills.
There is a noticeable amount of flanging on these notes. By the way, this song has two bass tracks by Miller.
Now a word about how to set up effects for bass. If you can split the signal, somehow (using a mixing board, or a computer-based mixing board), have the frequencies of 500Hz and above routed to your effect processor, and still have the bulk of the bottom end (300Hz and below) non-processed (a straight sound) you will likely have a killer sound.
This is because you have retained your bottom end and are only putting effects on the top end of your signal. Some recording engineers do this as a matter of practice on certain instrument recordings.
It is a bit more technical and complicated, but sometimes you have to go there. However, most effects, for the bass, process the entire signal, which is why it is generally best not to use them, except in isolated cases.