An investigation has been launched into the blaze which happened at around 1am on Saturday in Morden Walk.
It caused damage to the front door and kitchen window and the inside was affected by smoke damage. A rubbish bin, fencing and fuse box were also damaged.
The occupant of the flat who escaped was uninjured.
Firefighters who were called to extinguished the blaze said it had been started deliberately.
“An arson investigation has begun and we’d like to speak to anyone who saw the fire being started or anyone acting suspiciously in the area at that time,” said an Avon & Somerset police spokesman.
“Anyone with information should contact us on 101 and quote 76168/14. Alternatively, if you want to remain anonymous, contact Crimestoppers on 0800 555 111.”