Bailey first struck after four minutes, thundering in a shot from outside the box and from a tight angle past keeper Oliver Baumann.
The 23-year-old winger then intercepted an inexplicable 30-metre back pass from Andrej Kramaric to beat the keeper again.
Leverkusen, who were missing half a dozen players to injury and COVID-19, were caught napping when Christoph Baumgartner was left unmarked to charged forward and curl in a shot to cut the deficit in the 50th.
Leverkusen's 17-year-old Florian Wirtz, however, restored their two-goal lead five minutes later with a solo effort before Hoffenheim's Florian Grillitsch was sent off with a second booking in the 65th.
A stoppage-time penalty from Lucas Alario sealed their seventh win in the last eight games, and they leapfrogged Bayern Munich into first place on 25 points.
"This is certainly worth something," said midfielder Julian Baumgartlinger. "We all know how difficult it is in this league with so many tough teams to be at the top."
"It is a very positive snapshot of the moment, but we still need to value it."