The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in his Od Yosef Hai (Parashat Toledot), writes that one should not wash the morning Netilat Yadayim with water that had been in a restroom, as it is considered contaminated. Hacham Ovadia Yosef, in Yabia Omer (vol. 3), disagreed, and maintained that such water may be used. Preferably though, one should not use this water.
The Kaf Ha'haim (Rav Yaakov Haim Sofer, Baghdad-Jerusalem, 1870-1939) ruled that water that had been in a restroom may be used for the morning washing, but no Beracha should be recited when washing with this water. Given the different opinions that exist regarding the validity of this water, the Kaf Ha'haim applied to this situation the famous rule of "Safek Berachot Le'hakel" – that a Beracha may not be recited when it is uncertain whether it is required. However, Hacham David Yosef, in Halacha Berura, disputes this ruling, and maintains that a Beracha may be recited. As a general rule, when there is a dispute among the Poskim regarding Netilat Yadayim before bread, that form of washing is acceptable for the morning washing, and so one may wash in the morning with water that had been in the restroom, as there is a debate concerning the validity of this water for washing before bread. Moreover, it is possible that the Kaf Ha'haim would not apply his ruling to modern-day restrooms, which are cleaner and might not have the same status as the restrooms of old. And, it is possible that the Kaf Ha'haim referred only to water that was prepared to be used for cleaning oneself after using the restroom, not to other water.
Some Poskim maintained that if a person passed away in the neighborhood, near one's home, containers of water that had been prepared for Netilat Yadayim should not be used. If, however, one uses this water, he has fulfilled the Misva, since strictly speaking, the only problem with this water is that it is deemed unfit for drinking.
Water that was underneath a bed when somebody slept should not be drunk, and preferably should not be used for Netilat Yadayim, though one may wash with this water if necessary, and a Beracha is recited.
Summary: Although it is preferable not to use for the morning Netilat Yadayim water that had been in a restroom, such water may be used if necessary, and the Beracha is recited. This applies also to water that had been underneath a bed while somebody slept.