why does huck look for Miss Sophia's Bible?
Miss Sophia asked Huck to go back to the church to retrieve the Bible she had left there after church that morning. She probably didn't want to have to explain to her family why she needed to leave the house on Sunday afternoon when it was hot and time for napping.
When Huck finds the Bible, he discovers inside it the note that was left in it by Harney Shepherdson. Since Huck didn't realize who was the author of the note at the time, he didn't feel any reason to admit to Miss Sophia that he had seen and read the note. Later, as Huck was trapped in the tree waiting for the shooting between the Shepherdsons and the Grangerfords to end, he recognized "that that piece of paper meant that Miss Sophia was to meet Harney somewheres at half-past two and run off;" and regretted having been involved.