This is a very rough drawing of what I have in mind.
This would be enclosed in a sort of box with say around 15 bottles per level.
Each level would be attached to the back bone water supply with flexible hose so you can pull it out to stack bottles.
To use you would fill the reservoir at the bottom with sterilising agent + water. The pump would then pump the agent into the bottles. After a minute or two switch off the pump, use the tap to drain out the sterilising agent. Then fill the reservoir with water, switch on the pump and it rinses the bottles. Just leave the bottles in the rack to drain and you are ready to go. I was also thinking of space in the enclosure for the other bits and pieces that need to be cleaned.