Williamson, the 2004 Olympic bronze medallist, was beaten by five points in the final by former world champion, Italy's Natalie Valeeva.
Simon Terry won the bronze in the men's tournament when he defeated Italian Marco Galiazzo, the former Olympic champion, in the third place shoot-off.
France's Romain Girouille took the final 112-107 against Canada's Crispin Duenas.
Terry then joined Alan Wills and Larry Godfrey to take silver in the men's team tournament, losing to top seeds India in the final.
The women's trio of Williamson, Charlotte Burgess and Amy Oliver took the bronze medal when they beat Colombia in the third place shoot-off.
Britain new performance director Sara Symington said: "It's been a fantastic performance by both Alison and Simon and we're all really pleased for them.
"Alison has been competing at the highest level for nearly 20 years now, and it says so much about her attitude and determination that she still has the hunger for success."