The Herd went into the game atop the English Premier Ice Hockey League after beating Manchester Phoenix the previous night.
But they were always behind against Bees from the moment Lukas Smital struck late in the first period.
Martin Masa doubled the advantage at the midway point before Joe Rand got Bison on the scoreboard.
Any hopes of a comeback were ended by a dominant final stanza from Bracknell, who scored three times through Scott Spearing, Shaun Thompson and Pavel Strycek.
Bees will be hoping to continue their fine form when they face Manchester in a double header next weekend.
Gareth Cox's men travel north on Saturday evening (7pm f/o) before hosting Phoenix on Sunday (6pm f/o).
* SEE THIS WEEK'S NEWS FOR BEES PICTURES AND REACTION.