In rodeos, to bulldog an animal is to rope it and wrestle it to the ground. This has been done since ancient times, but the first modern cowboy to bulldog a beast was Bill Pickett, born 1870 in Texas. This black cowboy would ride his horse up to about five feet from the animal, jump onto its back, and grab one horn with each hand to twist its head back toward him. Then he made up for his being only five foot seven and 145 pounds by taking a tip from the dogs and actually biting the bull/steer on its lower lip or nose, to render it frozen with pain and thus more docile. After this, he could usually throw himself and the steer backwards or sideways to the ground. This technique was developed while herding cattle out on the ranch, but proved spectacular in rodeos as well.

Not too many other bulldoggers use that part of the "Dusky Demon"'s techique, but the event has kept the common name "bulldogging," though rodeos officially call it "steer wrestling" now. The modern bulldogger jumps onto the steer from his horse, tries to put his feet down to get the running animal stopped, and then wrestles the animal to its side with all its legs pointed in the same direction -- with times for 5 to 8 seconds for the best bulldoggers!

Sources:
Carlson, Laurie Winn. Cattle: An Informal Social History. Chicago: Ivan R. Dee, 2001.
http://www.cs.uh.edu/~clifton/pickett.micro.html
http://www.toptags.com/aama/bio/men/bpickett.htm
http://www.virtualtexan.com/readingroom/books/pickett/pickett1.htm
http://www.virtualtexan.com/readingroom/books/pickett/pickett3.htm