Atkin arrived in Spain in a confident mood having won her first-ever World Cup gold in Silvaplana earlier in the month.
And she carried that form over into the World Championships as she followed up her third place in Saturday's qualification by finishing in the same position 24 hours later with a score of 83.20.
Gold went to Tess Ledeux of France with a score of 85.60, while Swede Emma Dahlstrom was second on 83.80, while fellow Brit Madison Rowlands was 17th.
Despite Woods leading after round two, the men's event was won by Mcrae Williams with a score of 93.80, with fellow American Gus Kenworthy claiming silver with 91.80 points.
And third place and the bronze medal was secured by Woods with a total of 90.40, adding to the slopestyle silver he won at the 2013 World Championships.
Read the original article on Eurosport: Woods and Atkin claim slopestyle bronze medals at World Championships