Make the brine: Combine the vinegar, sugar, mustard seeds, 2 teaspoons salt and the bay leaves in a medium saucepan. Bring to a simmer over medium heat; cook, stirring to dissolve the sugar, about 5 minutes. Remove from the heat and let cool completely.
Meanwhile, bring a large pot of water to a boil. Cut the corn crosswise into 1-to-2-inch pieces with a serrated knife. Add to the boiling water and cook until crisp-tender, about 5 minutes; transfer to a colander using a slotted spoon and rinse under cold water until cool. Add the bell pepper and celery to the boiling water and cook 2 minutes; drain and rinse under cold water until cool.
Pack the vegetables and jalapenos into a 1-quart jar, then pour in the brine. Cover and refrigerate overnight or up to 1 week.