I heard rumors that after walking into a bathroom, nowadays, you're required to wash you're hands three times (as in, I've seen some Rabbi's do this: after just walking into a bathroom to get something, he washed his hands 3 alternating times).
I also heard (and experienced) that if there's a partition between you and the actual bathroom, you can wash you're hands there, even for bread and davening. I'm not sure though, as to the extent of the partition required. In the bathroom at the shul where I go to, they have the netilas-yadayim cup in a sink thats inside the actual bathroom, with inly a partition seperating between it and the urinal, and the other toilet is right next to it (but that was is partitioned off fully), would something in that case still be considiered a valid partition, even though it only blocks the urinal from one side, but you can still see it in the front, or does the partition have to block it from all directions, or is only a closed door sufficent?
Basically: whats the extent of the partition needed to wash your hands in a bathroom for bread or davening without any halachic concerns whatsoever