The Scholars mention that it is recommended for a person to enter the washroom using the left foot and to exit it using the right foot. Although there is not a specific evidence to prove this etiquette, it falls into the general evidences that a person begins with the right when performing honorable acts and begins with the left when performing less honorable acts.
Imam al-Baghawi (may Allah have mercy upon him) said: “And when entering the washroom, he begins with the left foot. If he exits, he begins using the right foot” [Sharhus-Sunnah (1/424)]
Imam an-Nawawi (may Allah have mercy upon him) said:
“Our companions and other than them from the Scholars say that it is recommended to begin with the right side in every thing which is honorable, like performing wudu, ghusl, wearing clothes, shoes, Khuff, pants, entering the masjid, using the miswak, putting on kohl, clipping the nails, trimming the mustache, plucking the underarm hair, shaving the head, giving the salutations in the prayer, exiting the washroom, eating, drinking, shaking hands, touching the black stone, taking, giving, and other than that from what is similar in meaning. It is recommended to precede the left side in the opposite of that like blowing one’s nose, cleaning oneself after using the washroom, entering the washroom, leaving the masjid, removing the khuff, the pants, the thawb, shoes, and performing things which are filthy and what is similar to that. The evidence for this principle are many Ahaadith reported in the Saheeh. From them is the Hadith of ‘Aisha (may Allah be pleased with her) who said:
كان رسول الله صلى الله عليه وسلم يعجبه التيمن في شأنه كله في طهوره وترجله وتنعله
The Messenger of Allah loved to begin with the right while putting on his shoes, combing his hair, in his purification and in all his affairs
Reported by Bukhari and Muslim.
on the authority of ‘Aisha (may Allah be pleased with her) who also said:
كَانَتْ يَدُ رَسُولِ اللَّهِ صلى الله عليه وسلم الْيُمْنَى لِطُهُورِهِ وَطَعَامِهِ وَكَانَتْ يَدُهُ الْيُسْرَى لِخَلاَئِهِ وَمَا كَانَ مِنْ أَذًى
The Prophet (ﷺ) used his right hand for getting water for ablution and taking food, and his left hand for his evacuation and for anything repugnant. Reported by Abu Dawood and others with a Saheeh Isnad.
on the authority of Hafsah (may Allah be pleased with her):
أن رسول الله صلى الله عليه وسلم كان يجعل يمينه لطعامه وشرابه وثيابه، ويساره لما سوى ذلك،
That Messenger of Allah (ﷺ) used to use his right hand for eating, drinking and wearing his clothes and used to use his left hand for other purposes. Reported by Abu Dawood and others with a Jayyid Isnad” [al-Majmoo’ (1/418)]
Imam ash-Shawkani (may Allah have mercy upon him) said: “As for beginning with the left foot when entering the washroom and the right foot when exiting, then it has an angle of proof due to the right side being for that which is honorable and the left side for what is not honorable. What proves that in general has been reported” [Sayl al-Jarar (1/64)]
Shaikh al-Albani (may Allah have mercy upon him) said: “As for entering the washroom, then I do not know a proof for it [until] now. Perhaps it is comparable to [the etiquette of] exiting the masjid. And Allah Knows Best” [al-Irwaa under Hadith no. 93]
And Allah knows best
Faisal bin Abdul Qaadir bin Hassan