The impressionist told the Radio Times that he had danced around his bedroom in the middle of the night a couple of nights before his first performance out of concern that he would forget the steps.
Bremner said: "Two nights before my waltz, I woke in a sweat, panicking that someone had broken into my head and taken out the 'choreography' file.
"I got up, plugged in my iPod and danced around the bedroom, bouncing off the furniture. After waltzing, I slumped back into bed."
Bremner also said that he had been trying out dance steps in a variety of locations including "the supermarket, hotels [and] train platform[s]".
Bremner and professional partner Erin Boag performed a quickstep to a song from the Fred Astaire musical Top Hat on last Saturday's show.
The pair scored 31 out of 40 points - their highest mark in the competition so far.
Strictly Come Dancing continues next Saturday (October 22) at 6.25pm on BBC One.