Is it worth buying the JR Pass for Kyoto?

No. The JR Pass is for long-distance travel between cities. It does not cover most local Kyoto buses or subways.

Should I rent a bike?

Only if you are comfortable riding on narrow streets with traffic. The city is flat, but it gets very crowded, and many historic sites restrict bike parking.

3 Days in Kyoto: A Practical Itinerary

Spend your first day in Higashiyama to hit the iconic temples, your second day in Arashiyama for nature, and your third day exploring the downtown markets and Fushimi Inari. Use the bus and subway systems to navigate, and start your days at 7:00 AM to beat the massive crowds.

Master the transit card. Download the Suica or Pasmo card to your Apple Wallet or Google Pay immediately. You will use it for every bus, subway, and train ride. It saves you from buying individual paper tickets.
Beat the rush. Kyoto is extremely popular. Aim to be at your first major stop by 7:30 AM. By 10:00 AM, the most famous spots like Kiyomizu-dera will be shoulder-to-shoulder with tourists.
Use buses and subways together. The subway doesn't cover everywhere. Use the Kyoto City Bus for mid-city travel, but be prepared to stand. If you are a group of 3 or 4, taking a taxi for short cross-town distances is often the same price as four bus tickets.

Is it worth buying the JR Pass for Kyoto?: No. The JR Pass is for long-distance travel between cities. It does not cover most local Kyoto buses or subways.
Should I rent a bike?: Only if you are comfortable riding on narrow streets with traffic. The city is flat, but it gets very crowded, and many historic sites restrict bike parking.