Like all Shinto shrines, Fushimi Inari Taisha is always open, and at dusk you can find Japanese who appear to be jogging along the hilly path. After nightfall, the gaijin return from dinner and take pictures of the torii all lit up. You will be well-served with a tripod, although a f/1.8 50mm Canon prime lens at 1/50 with ISO 3200 generally worked well for me. Consider photgraphing at dusk, however, as the lights are on but there is still enough light for ambient light to avoid the harsh shadows at night.
No Kyoto sight-seeing busses go to Fushimi Inari, although it is within walking distance of Tofukuji. If you are coming from the late-closing Kiyomizudera, you can take the expensive Keihan line from Keihan Gojo station; if you are elsewhere you may want to take the JR Nara line.
The Japanese website looks fairly comprehensive if you are literate. There appears to be a list of festival days.