Whew! A lot of effort to get one or two shots. I wanted to test the limits of my new Canon RF 100-500mm telephoto lens, and this did it. I had taken pictures with a solar filter and was comfortable with it. You can use this link to find a place near you where the International Space Station (ISS) can be viewed transiting across the sun: https://transit-finder.com/. In doing so, you learn that the actual time that the ISS crosses the sun, traveling at about 17,000 miles per hour, is 1.35 seconds, making it easy to miss. To be sure that you catch it, you need access to the most accurate time, here: https://time.gov/. Looking into this further, I used the transit finder along with weather prediction to select a day with clear skies projected and where I would not have too far to drive. Yet I learned that the ISS path can waver ever so slightly and you need to re-do the transit analysis the day prior to your shoot, to be sure of where to stand. How sure? From what I read, within 100 feet of the projected transit line.
Setting up about an hour beforehand is advised. Take practice shots of the sun (with the solar filter on; I used an iOptron 70mm White-Light Solar Filter, $49 from B&H). Then turn off the camera a while and let the sun move across the frame, then turn on again to get the feel of the sun's movement. You don't want to fuss with that, when the moment of truth arrives. I had the camera on a heavy metal tripod with a big ballhead (RRS BH-55) mount and a remote switch.
Most web sites will suggest using a focal length of 1000-2000mm, so I was pushing it with a 500 mm focal length; on a zoom lens no less. After testing many parameters on my Canon R5, I used autofocus on "expand AF area" which would nicely grab an edge of the sun for focus, maximum aperture for the lens of f/7.1, 1/800 sec (minimum really), and ISO 100. I kept the stabilizer on, which I found to help with the slight wind. I set the camera on JPG max resolution (45 Mp) and high speed continuous shooting which, as far as I could tell when holding down the remote shutter release, would keep taking JPGs until the battery ran out. It was useful because I wound up taking over 240 continuous shots to be sure I captured the ISS transit.
The moment of truth: The transit finder gives you the time of the transit, at your selected point, to the hundredths of a second. So you need your cell phone in one hand, open to the time.gov site for your time zone, and the remote shutter release in the other hand, having a few minutes earlier lined up the sun in the middle of the screen to grab autofocus. Twelve seconds before the supposed transit, I started taking photos and continued for another 10 seconds or so after the supposed transit. The ISS itself is way too small to see on the camera monitor afterwards, so you don't know if it worked until you get home and load it onto your computer.
There was a moment of elation when I saw that, indeed, I had captured the transit in a cluster of images in the middle of my grouping. The elation gave way when I tried to figure out how to blend them into the classic view of the multiple ISSs images going across the sun. The simplest way that worked for me was taking the advice from this link: https://www.thelondonastronomer.com/it-is-rocket-science/2017/6/26/imaging-and-processing-solar-and-lunar-transits-of-the-international-space-station (or Google: london astronomer solar transit of iss). There was variation in sharpness of the ISS from frame to frame, which I attribute to being at the absolute limit of what the lens could do. Also, taking the shot at 5:44 PM, the sun was low in the sky, making the sun appear larger but enhancing atmospheric-induced aberration. Still, I was pleased to capture the moment of truth.