Can I use a Japan Rail Pass for Kyoto buses?

No. The JR Pass only covers JR trains, not the city buses or private lines like the Keihan or Hankyu.

Is it worth renting a bike?

Only if you stay in the central flat area. Kyoto is quite hilly toward the East and Northwest temples, making cycling difficult for a beginner.

Kyoto: A 3-Day Plan for Temples and Gardens

To see Kyoto's best, group your visits by geography to avoid crisscrossing the city. Dedicate one day each to the East (Higashiyama), the Northwest (Arashiyama/Kinkaku-ji), and the South/Central districts.

Buy a Keihan or ICOCA card immediately. Do not buy single-ride tickets. Get an IC card at the station for seamless subway and bus boarding, as Kyoto buses are the primary way to reach most temple gates.
Start your days at 7:30 AM. Most popular temples open at 9:00 AM, but popular spots like Kiyomizu-dera are crowded by 10:00 AM. Arrive at the gates 30 minutes before opening to get a clear hour of peace.
Use the bus-subway hybrid route. Take the subway as far as possible to beat surface traffic, then switch to a local bus for the 'last mile' to the temple.

Can I use a Japan Rail Pass for Kyoto buses?: No. The JR Pass only covers JR trains, not the city buses or private lines like the Keihan or Hankyu.
Is it worth renting a bike?: Only if you stay in the central flat area. Kyoto is quite hilly toward the East and Northwest temples, making cycling difficult for a beginner.