I haven't seen anything like this posted before, so I thought I'd share it.
The blue bulb and white stem came as a cleaning tool for a crappy non-LDD doll (one of the only good things from that order. Stick with LDD for inexpensive dolls guys!) You can get a similar bulb by searching for "bulb syringe" or "battery filler bulb", though I can't promise it will fit the tube like this. The clear hose is standard aquarium air tube. The 'T' came with the walmart air pump I got for drying. The blue cylinder with the white arrow is the magic part. It's a one way air valve from walmart. I think its called a check valve. It lets air flow in the direction of the arrow and blocks flow in the other direction.
Here's why I like it. You plug the open end of the valve and fill the bulb, then place the end of the tube in the orifice to be cleaned, unplug the valve and squeeze the bulb (duh, right?) Then the magic happens: when you release the bulb, air gets sucked in through the valve, instead of sucking dirty water back into the bulb. Then you can squeeze the bulb again (which should still be about half full) for more cleaning without removing the tube. Even if you empty the bulb in one squeeze, you dont have to keep the bulb squeezed to keep the bulb clean. Added bonus: you can push the tube all the way to the end of the orifice, no supplied cleaning tool I have even comes close.
I tried attaching another hose to the valve so I didn't have to remove the cleaning tube from the doll for refills (put the valve tube in the cleaning water), but it filled to slow through the air valve. I'm currently on the lookout for a cheap liquid/air one-way valve to fix that. I'll share if I find one.
It may seem like I'm over thinking this, and I probably am, but it has sped up and simplified clean-up. The best part is, all I had to buy was the valve. If you use an aquarium air pump for drying, you could put this together for less than $10 (maybe $5 with a cheap bulb). If not, add about $5 for a 'T' and some tube.
Edit: I found the bulb I have. It's a bit more expensive than the other options, but you can find them by searching for "enema bulb" or "rectal syringe"
Enjoy!