finding a publisher for a duet arrangement?

[Nemo]

Hi, since i LOVE flight of the bumblebee, i've had it in my computer in several different formats. while looking at that outrageously abusive treble staff, i thought of making a duet arrangement. today i printed the first copies of it and my teacher says they're great.
I made it so that there is a great amount of changing melodies from piano to piano(4 hands, 2 pianos) and one piano helps the other with the chords while it does a fast part. its really good but i'm workign to make it look even better.
my teacher said that i could get this published. and that got me thinking, can i do that? and how? not really about the money as these got for like $4, but its more about helping the people. i find it 200% easier to do in a duet, specially this way i've arranged it, and i'm positive that people would like it.
So here are the questions:
1)Is it legal to try and publish it? - I got the transcription online somewhere and wrote it into the piano program.(solo version) The duet version, with all of its arrangements and hours of work were by me alone.
2)Who should i get to publish it?
3)How do i reach them?

Thanks for the help:-)

[88keys]

It's legal. Rimskey Korsakov died in 1908, so his music is in public domain.

If money isn't important for you, my suggestion would be to open your own website and publish the arrangement there. You can either purchase professional web space (it cost around $50 a year) or settle for a free page supported by advertisements.

Getting yourself published with a real-world publisher would, overall, cost you much more. And the risk of rejection is always high - especially for a piece so short.