I have to travel alone at night (by bicycle or foot, at about 25-50 min.) to perform Fajr or Isha prayer in the closest Mosque. Would it be correct to travel alone for the purpose of praying in a mosque?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Congregational prayer is obligatory on whomever hears to the call for the prayer and has no excuse not to attend.

Ibn Majah reported that Ibn Abbas (Radiya Allahu Anhu) narrated that the Prophet (Sallallahu Alaihi wa Sallam) said: “Whoever hears the caller for the prayer and does not come to it then his prayer is not valid unless he has a sound excuse.”  And in the narration of Abu Dawud, “Whoever hears the caller of the prayer and no excuse prevented him (that) from answering his call,” they asked: ‘What is the excuse?’  He said: “Fear or sickness.  Then the prayer he performed (thereupon) is not accepted.”

Therefore, if the closest mosque to you is far away from you, to an extent that you cannot hear the call for the prayer, or if the road to it is fearful, then it is not obligatory upon you to go to the mosque.  It could become unlawful for you to go if you fear death or severe harm.

However, if you do not fear any harm, then it is possible for you to go to the mosque on foot or by bicycle.

Allah knows best.