The best I can do is show a picture we made for the website:
http://www.montreur-etoiles.fr/fusees_presentation.pdf
basically all you have is a Schrader adapter to connect to the bike pump, a wooden board with a couple sideboards acting as legs, and that, well, thing.
I guess it was not custom made ; my predecessor found the supplier online, but that was about 10 years ago. He bought three or four and they still work very well; you just have to replace the o-rings when they start wearing out. We would also have to swap between 11- and 12-size rings because depending on weather conditions they will be more or less dilated, and hold on to the rocket more or less.
So what holds the rocket to the launcher is the O-ring itself : we stick it inside of the neck of the bottle. There is no specific nozzle, just the bottleneck. The friction holds the rocket to the launch pad; liftoff occurs when the pressure inside the bottle is stronger than the friction.
Pro: super simple and fail-safe, esp. during events where we may have just a few minutes to setup, and zero turn-around time if something goes wrong.
Con: If the o-ring is too small / not dilated enough, the rocket will not stick well and take off too early; if it is too large, well, you can reach pressures of up to 150 psi and it still does not launch, so you try to abort in some way (we've never had an accident, but are in no rush for that). Anyway when we've had super-high pressure launches, the water comes out in explosive fashion and it does not fly very high.
The other con is that you never know for sure when liftoff will occur, aside from a slight quivering of the bottle just seconds before.
