When to go
Best season
July, August, September, October
If the winter has been a big one, there will most definitely still be snow in July and possibly into August. The summer months are the only time the area is accessible.
Pay attention to conditions before your trip, and bring appropriate gear. You may need an ice axe and crampons if there is still snow getting up to Bishop and Thunderbolt Pass.
The view of the Sierra Nevada from this spot is incredible! And, catching the light of a sunset on the many peaks visible in the distance is an unforgettable experience!
Field tips
Bring everything you normally would for backpacking (tent or bivy, sleeping bag, pad, puffy jacket, stove, bear canister [recommended], food, water bottle/bladder, filtration, etc.). Aside from camping gear, bring your camera, a variable focal length lens, and a lightweight tripod if you have one.
Mosquitoes can be pretty bad, especially on the way up to Bishop Pass, so have that bug spray and head-net ready! A compass will also come in handy. The compass app on your phone is sufficient.
Bishop Pass is at nearly 12,000 feet, and Thunderbolt Pass is almost 12,200 feet. If you are susceptible to altitude sickness, look into acetazolamide (generic for Diamox), and perhaps bring some with you. If you aren't feeling well, do not continue. Altitude sickness can be very serious. Only going back down will alleviate the symptoms.
If you don't have a lightweight tripod, you can improvise a tripod from gear you already have, or even from natural features. I did not have a tripod for this trip, and used rocks in the area to set up a shot. I was even able to get photographs of the Milky Way on this night with nothing more than the camera body on a rock with the lens propped up on a smaller rock.
The light can be tricky in an area such as this. The light on the peaks in the distance and in the sky can make it difficult to capture details in the shadowed foreground. Try bracketing exposures and combining later to make it look like your eyes saw it!