Sareitha was not particularly strong in the One Power. Her level of strength is described by "The Wheel of Time Companion" as 26(14) which is a middle level in Aes Sedai hierarchy (not particularly weak, but also not remarkably strong). With this level of strength she was unable to open alone a suitable gateway to Travel.
Ebou Dar Edit
She was allied with the Salidar Aes Sedai.
She was sent to Ebou Dar as part of the embassy from Salidar to Tylin Quintara Mitsobar, the Queen of Altara. While inside to Tarasin Palace in Ebou Dar, she faced off against the White Tower embassy as to whether Matrim Cauthon should be returned to the White Tower.
She Traveled with the the rest of the group led by Nynaeve al'Meara and Elayne from Ebou Dar to the Kin's farm with the Bowl of the Winds. Sareitha made it known that she feels Aviendha's name should be in the book of novices. She felt the Kin cannot be trusted because some of them claim to be a hundred years older or more than any known living Aes Sedai. She didn’t believe that can be possible and so didn’t trust them. She then journeyed to Andor with the rest of the group.
To Caemlyn Edit
She moved through the city with Elayne Trakand when Elayne was out in Caemlyn greeting the people. She was the only Aes Sedai who thought that Doilin Mellar acted as a hero by rescuing Lord Luan Norwelyn's men, even though Luan had not yet declared his support for Elayne. Perhaps this reflects her relative youth when compared with the other Aes Sedai.
In the Blue Reception Room in the Caemlyn Palace, Sareitha and Careane Fransi threatened the mercenary captains present about the power of the White Tower in order to help Elayne bring them under control.