Yes, it's simple. I just whispered, "Are you going to let us pass big fellow."

It sounds like you did everything right in your encounter with the two Bison along the trail in Sentinel Meadows. I believe the Park Service regulations is a distance of 25 yards.
I've had numerous encounters with Bison over the years in Yellowstone and have learned that if I leave them alone, they leave me alone. Recognizing when one might be agitated is helpful too. If you see one lift its tail and you are in the vicinity, it is letting you know that it takes exception to your presence and it is best to give it plenty of room. I've had to make my way through herds occasionally over the years too. Once, on my first Mary Mountain hike, there was a large herd at the west end of Hayden Valley I had to negotiate. A second herd was encountered when I did my hike along the Old Fountain Trail that crosses the Madison Plateau. I've found that cows and calves tend to get out of your way as you pass. Bulls, are another story, particularly if they are in the rut. My son and I had a lone bull get after us on the Wapiti Lake Trail as we were returning to the trailhead at Canyon a few years ago. At the same trailhead on another trip, my family was getting ready to head into the backcountry for a couple nights at Ribbon Lake when two bulls suddenly appeared, getting after one another. One of the bulls disengaged from the other and essentially came after us, leading us to maneuver around the vehicles in the lot by the trailhead. It is all just part of hiking/backpacking in Yellowstone, and one of the reasons it is my favorite place to spend my free time.