A traditional approach to composition is to play/write out all the parts for the piano and create what is called the piano reduction score. From this you extract and assign parts for the ensemble. An analogy to painting: sketch the basic form on the canvas then work each part (usually from background to foreground) with color, shade, highlights etc.
In your case you are composing for "Piano, Drums and Bass Guitar". I would suggest working out the melody, harmony, and rhythm on the piano first. Once you have your patterns translated into beats, notes, and measures then start your recording from the beat up. That would be drums first, then bass, then piano. If you would prefer doing it another way at least provide yourself with a 'click' track as a beat reference so you can keep time as you lay in the remaining tracks. When you are done recording all the parts, just remove or mute the 'click' track before making the master mix.
When I compose I try to imagine the whole thing as it would sound when it is completed or I may already have this image in my mind and find myself taking it apart to see how it can be built. Another approach is to start with a simple melody and build on this to create the harmony (chords or extra voices) and development as variations or verses, chorus or bridge elements, all depending on the style etc. A good example of the additive method would be the fugues, canons, or preludes of J. S. Bach.
Since your target is Pop/Jazz, don't forget that in traditional jazz, everyone in the ensemble may take a solo. I sort of think this is dependent on how many players are in the group, and their ability to solo and improv. I wouldn't recommend everyone taking a solo in a 12 piece band. The solo may be different every time, or the composer may leave instructions on setting some musical boundaries on the solo, or even actually spell it out. Another thing that is cool about this is that you can make this a variable part of the piece, for example you may have 2 extra minutes to kill to complete your set, so why not extend the piece with some more improv and solos?
As the piano historically has been a very useful composing tool because it can cover both the range of notes of the orchestra as well as the dynamics ("quiet" to "loud, aka pianoforte) so too the modern day synthesizer with a multitrack recording device/software can be an extension of this. A good synth today will have keys weighted like a piano and offer a compatible action with the addition of extended voices (1000's). Linked to a multitrack recording machine or computer running recording software, the composer can now model, and mix his idea with more clarity than with a piano score.
Another approach is to use automated notation software with sample sounds such as Sybelius or Finale, which allows for notation and hearing and making the whole process of copying parts for each performer so much faster and easier than hiring a copyest.
Often the compositional process is more about the composer's process and how the composer has developed the optimal workflow to accomplish his or hers vision. Hence, every artist faces learning a methodology that embraces their journey. We all start out with learning the same process but end up changing it to accommodate our personal way of doing things.