Another reason that you worm birds orally is that you know they got properly wormed, no guesswork about it.Not everybody is able to give it to them orally, if that is the case, here is the water dosage.
Adding wormers to water for birds to drink isnt very effective. You dont know if they'll drink it, or drink enough of it to be effective, sick wormy birds dont drink at all and birds drink less in cooler temps.