Start with this lot: The spanner is a cycle pedal spanner size 15 - pops into the top of the bottle a treat, holds the nut snugly and doesn't foul on the bottom of the bottle like a normal spanner. Plumbers tape round the thread because I am that OCD

Hold the nut and screw the pump in till reasonably tight - this is very easy with only 1 pump fitted but is a right pain with 2 as you will get to a point where you can't move 1 pump past the other.
Next double loop the cord like so: Slightly stiff cord and/or wet cord helps at this point so you can lower it into the bottle without losing the loops. I use the spanner again to push the loops down over the nut like so: All you need to do now is hold one end and pull the other to tighten the nut - simples.
Top tip - don't pull with Sampsonite strength trying to get a watertight seal - you will snap the threded section off the back of the pump...ask me how I know

To clean the bottle the quickest way I have found is to mix some baking soda with a little water to make a paste then use that on a sponge and it should come up white or at least more white than it was!