The victory, coupled with Old Centralians' failure to pick up the extra point at Salisbury, means Bracknell are five points clear of their nearest rivals at the top of South West One East.
That lead could be cut on Saturday as Cents play their re-arranged game with Newbury Blues but only a hugely one-sided score would prevent Bracknell ending the year on top.
The Lily Hill men were always in front at Cheltenham after Ceri Cummings kicked a couple of early penalties.
Mackay and Nico Maybury both touched down before the break to put Bracknell 18-3 ahead and George Milligan all but wrapped up the win when he crossed on 56 minutes.
The visitors did not secure the bonus point until late in the game though as Mackay crossed for his second score.
Bracknell's first game of the new year sees them go to Coney Hill on January 5.