Washing Hands After Entering the Bathroom

If someone enters a bathroom that contains a toilet but does not relieve themselves, do they need to wash their hands? If so, how many times?

One should wash their hands once. Some are stringent and wash three times.

In Mishnah Berurah, Siman 4, Se'if Katan 39, a dispute is brought between the Heichal HaKodesh and the Magen Avraham regarding the rule for entering a bathroom, even if one does not relieve themselves, due to the evil spirit that resides there, as written in Mishnah Berurah, Se'if Katan 40, whether one needs to wash once or three times. Some are concerned with the opinion of the Heichal HaKodesh. It is explained in the Gemara Berachot 26 that a Persian toilet does not have the status of a toilet, and so ruled the Shulchan Aruch in Orach Chaim, Siman 83, Se'if 4: "A toilet that is in a pit, and its opening is four cubits away from the pit, and it is made on a slope so that the excrement rolls and falls immediately far away, and also the urine immediately goes down into the pit, is considered closed and it is permitted to read there, if there is no bad smell and no one urinates outside the pit." The Chazon Ish, Orach Chaim, Siman 17, Se'if Katan 4, was uncertain about the status of modern toilets, whether they are like Persian toilets, since there the excrement was immediately absorbed into the depth of the earth, unlike modern toilets where the excrement remains until the water is flushed, and concluded that it is proper to be stringent.