How much time did Jesus spend in Gethsemane? In the four Gospels of the usual canon — Matthew, Mark, Luke, John, — only two of them mention any measure of time:


  Then He came to the disciples and found them sleeping.  He asked Peter, “So, couldn't you (all) stay awake with Me one hour?  […]”
  ― Matt. 26-40, HCSB
  
  Then He came and found them sleeping.  “Simon, are you sleeping?” He asked Peter.  “Couldn't you stay awake one hour?  […]”
  ― Mark 14-37, HCSB


In the narratives of those two books, he goes away to pray twice more.  In the book of Luke, only the final wakening of the disciples is described, and in the book of John their stay in the garden is mentioned but very briefly.
Estimating from the time of year — near the vernal equinox and on the summer side of it, — it could've been anywhere from a modern hour to half the night.

Do we have some more precise records which would indicate a timeframe there?
E.g. when he was arrested, or perhaps some non-canonized documents describing when they would've gone to the Mount of Olives?
The narratives at Luke 22:47-62 describing the arrest of Jesus and the denial by Peter before the cock crowed, give ample evidence that Jesus prayed at Gethsemane till early hours of Friday, counting from 0000 hours as per modern time-keeping system. (NB: The Ifugao of the Philippines state that cocks crow four times during the night with the third cockcrow at around four o’clock in the morning. Courtesy: Scientific American Blog Network)   

Luke 22:39 also states that Jesus had gone to Mount of Olives 'as was His custom' indicting that He used to pray for a long time.