It's called an Enteral Feeding Bag, and it usually hooks up to an Enteral feeding pump.
You can try a pharmacy for the bags. Just tell them you're trying to set up a drip system for your houseplants while you're away, or some such; and that you don't need the hypodermic needle, just the bag, tubing and flow adjuster. That might work.
Of course, if you manage to obtain an Enteral feeding pump, that opens up a whole new range of possibilities in that you could use a much larger source than just the bag and then through the proper use of T or Y fittings you could service a number of containers at one time.
Only the outside of the tubing connects to the pump which then moves the liquid through the tubing via a type of rotating cam. No liquid actually touches the pump itself.
And yes, you could use an Enteral feeding pump with a large water tank to water your houseplants while you're away. 8) 8) .
Finally, under no circumstances would I recommend anyone collecting or using 'used IV lines' for this purpose (no matter how much you think you've disinfected them first). There are enough dangerous and infectious diseases rife in the world (and especially in hospitals) and the last thing anyone needs is to contract one of them. That would sure put a kink in your refining plans.
Remember! You can incinerate Dental scrap before processing. You can't do that with plastic tubing.
Work Right. Work Safe.
Shaul