Hi Steph,
there are a lot of elements that go into a composition, even more if you are the one performing it...
firstly, there's the initial idea - that little seed that sparks the rest of the tune. It might be a melody, a chord, a couple of chords, a who progression, even a drum groove. For solo bass, it's often a little melodic figure that is easy to harmonise at the same time, or a couple of chords where the top note in each chord forms a melodic line.
Then there's the development of the idea - a great idea can be ruined by 'over developing', or moving on too fast from the initial idea. There are so many ways that a tune can develop - repetition, changing one part (phrasing, changing the octave, inverting the tune, reharmonising, keeping the chords and changing the melody, stretching it out or writing an 'answering' line for your initial idea)
Then (or perhaps before that, but for me it normally comes here) there are all the considerations about the form of the tune - is it going to be a verse/chorus alternating idea? will it just repeat and vary? will it be 'through composed', that is, will it just grow and change without much repetition, or will it be a minature, and stay as it is? Deciding on form will have a huge effect on how you write.
At each stage, think about the key that the piece is in - try changing it and see what the effect is? are there more or less open strings available? are there more harmonics available? I tend to write in the keys that allow me to use harmonics and open strings, just to save retuning or buying loads of hipshots like Michael Manring! :o)
Once you've got an idea, it's worth trying it in different rhyhmic combinations - what happens if you 'swing' it? what about trying to rephrase it in 3/4, 5/4, 6/8, 9/8? sometimes a melody that you're struggling with can come to life like that. what about playing it completely free rhythmically? music doesn't have to groove, even on a bass!
then there are the performance considerations - intro, ending, sound, seating postion, effects etc.
there's no set order to these things - for me, sound is often the first consideration and the piece springs from that. other times, I'll change it at the end and breath new life into a dull tune.
take it slow - these aren't rules, just areas to consider. Enjoy it, you're in charge, you make your own rules, you write what feels good, what sounds right to you and have fun doing it - it's not a competition, it's not about being 'the best' or the cleverest/fastest/trickiest/funkiest - all that is BS. It's all about being you, playing what's inside you. If that's two notes, play them like you mean them. If that's mad fast slap stuff, play it like you mean it. If you play for applause, that's all you'll get...
relax and enjoy
Steve
www.steve-lawson.co.uk