The crowds of pilgrims who had come to Jerusalem for Passover overloaded the system. Many of them likely slept in the open on the Mount of Olives and other places near the city. On Monday evening,
And he entered Jerusalem and went into the temple. And when he had looked around at everything, as it was already late, he went out to Bethany with the twelve. (Mark 11:11 ESV)
Luke tells us that it was His custom to do so.
And he came out and went, as was his custom, to the Mount of Olives, and the disciples followed him. (Luke 22:39 ESV)
Bethany, the village of Mary, Martha and Lazarus (John 11:1), was located on the eastern slope of the Mount of Olives about two miles from Jerusalem (John 11:1, 18). The photo below shows the Church of St. Lazarus at Bethany. The walk from the main street goes through a pleasant garden. This was the Jerusalem-Jericho road before the building of the tunnel and the new highway.
Here on the eastern slope of Olivet we find the traditional tomb of Lazarus. In the time of Jesus the mountain was likely filled with olive trees. Jerusalem may be seen only after one reaches the crest of the mountain.
Jesus also visited in the home of Simon the leper at Bethany, where a woman anointed his head with oil as He reclined at the table (Matthew 26:6-7).
Tradition places the ascension of Jesus on the top of the Mount of Olives, but Luke says it took place at Bethany (Luke 24:50-51).