Timing and order
Bamboo first in the morning (thinner crowds), then Tenryu-ji garden, afternoon Togetsukyo and the Katsura; if legs allow, monkey park or Okochi Sanso — pick one. One yudofu lunch, then stop.
JR vs Hankyu
From Kyoto Station: JR Sagano to Saga-Arashiyama, ~10+ minutes north to the bamboo. From Kawaramachi: Hankyu to Katsura, Arashiyama line — nearer the bridge. Riding both wastes transfers. City bus works but loses in traffic seasons.
Where to stop / what not to stack
The day stays in Arashiyama/Sagano. Not Kinkaku, Ryoan-ji or Kiyomizu. Torokko train or a boat — pick one; they are not a second sightseeing day.