You need to put a couple drops of mild soap in with the water. This will help break up the oil so it will mix with the water. If it isnt mixing good after that add another drop or two. I used dove soap that my wife had but I have a friend that uses dawn, lol.....
either soak neem bottle in warm water then put in nother container with warm water and neem and all is well,use soap if ya want to,but no need really,i do about 2 cap fulls of neem to a spray bottle of warm water and it breaks down just fine,then keep bottle in warm water before using,does not hurt anything either using warm water if spraying right before light out or early night or morning