How should I present my work to my advisor?
I think the advantages of showing it soon (i.e. unfinished) outweigh any disadvantages. The advisor may have some suggestions as you note and may point you to prior work that you may not be aware of. That could make further work more or less desirable, of course, but either way, it is good to know.
And, whether publishable or not, it may indicate that you are gaining needed insight into your field.
I think that very few advisors would not want to be bothered.