If a person went to the bathroom and then wishes to wash for a meal, the halacha differs from the usual, preferred method of washing hands after using the bathroom and is as follows:
1) One should first wash in a manner which is only for cleanliness, but not kosher before eating a meal.
One way to do that is not to use a keli, vessel, but to wash directly from the faucet. However, as there are opinions that a faucet is also considered a keli, one should first let the water run for a while, and only then wash, so that it should not be considered koach gavra, water coming from human power, which is the required way to wash for a meal.
Another option is that the hands should not be washed until the knuckles (which, according to some opinions, is considered a legitimate form of washing before eating a meal; rather, one should wash until before the knuckles. Then, one should make the brocho of Asher Yotzar.
2) Afterwards, the hands should be dried and then washed again, this time with a proper keli and in the manner one washes for a meal.
Those who are particular to wash their hands up to the wrists three times, alternating between hands, every time they come out of the bathroom may do so in the second washing (in addition to the required washing for bread on each hand two times, or according to Chabad custom three times, consecutively) in order to fulfill that custom.