Oddsmakers posted the three-year-old colt, who won last month's Arkansas Derby by almost 10 lengths, at the top of the betting line at 4-1.
Trainer Bob Baffert, already a three-time winner of the Run for the Roses, had less luck with his other runner, Liaison, which drew the outside pole in the 20-horse field.
"You gotta take what they give you," said Baffert, who is still recovering from a heart attack he suffered during the Dubai World Cup in March.
Union Rags, a winner in four of his six career starts, was listed as the 9-2 second choice after drawing the coveted post position four.
"The horses around him maybe don't have that much speed, so that pushes us closer to where Bodemeister will be," said trainer Michael Matz. "It looks like it came up OK; we'll have to be running from the start."
Take Care Indy, the surprise winner of the Florida Derby, drew three while the Irish-trained Daddy Long Legs, who secured his place in the $2.2 million race by winning the United Arab Emirates Derby, landed the dreaded number one hole.
It has been a quarter of a century since a horse drawn on the rails has won the mile and a quarter race.
Most of the favourites fared well in the draw. Gemologist, rated a 6-1 chance after winning the Wood Memorial, will break from 15, a wide barrier which should suit his style of racing, while Blue Grass Stakes winner Dullahan (8-1), drew five.
Hansen (10-1), the winner of last season's Breeders' Cup Juvenile at Churchill Downs, drew 14.
"I wanted 14 or 15 from the start, so I'm excited," said Kendall Hansen, who bred and owns the near-white colt.
A total of 21 colts were entered for the race with My Adonis listed as a reserve should any of the 20 runners scratch before Friday morning.