Josiah P. answered 07/01/19
Musician Experienced in Teaching Drums and Composition
In my own experience I haven't met any composers who encourage writing away from any instrument, even if it's not your own. Yes, it can be done but your compositions will simply come out better if you are composing at an instrument. It's also possible (and very convenient) to have a computer and and instrument with you while composing.
As far as methodology of composing, most texts suggest starting with melody and adding chords after. From there you can go to orchestration. Which instrument(s) should have the melody? Should there be a counter-melody? What is the bass instrument(s) doing? What is happening rhythmically? Of course, you can go the other way as well: Start with chords, then add a melody.
A fun exercise can be to write a contrafact (a new, original melody written over an existing harmony) then write a new harmony for your melody, then write a new contrafact over THAT harmony, etc. This can be done as much as you want and you'll see your composition evolve in front of your eyes. Many compositonal ideas can be gained from such an exercise.
In the end, whichever method YOU prefer most is completely fine. It can be very useful to use a variety of methods which will expand the ways in which you are able to create music.