Conway reached the under-70kgs pool final but lost out to German athlete Laura Vargas Koch. She recovered, though, to come through for bronze with victory over German Barbara Bandel by an ippon score.
The 26-year-old said: “I am happy with my performance overall. There are bits to work on and areas where I can sharpen up.”
Londoner Tom Davis also lost his under-81kgs pool final but was unable to win his subsequent bronze medal contest, losing by waza-ari to Alan Khubetsov of Russia.
Coach Kate Howey, Olympic silver medallist in Sydney, said: “This was a good day for Sally to restore some confidence following the Europeans. The result means she has qualified for the (IJF) Masters.”