Trim tough ends of asparagus and cut spears into uniform lengths, about 3/4 inch shorter than the inside height of the jars. In a large shallow dish, cover asparagus with ice water and refrigerate for 1 hour. Drain well.
Meanwhile, prepare canner, jars and lids. For instructions, please visit the Ball Canning website. In a small bowl, combine red and green bell pepper, jalapeño pepper and garlic. Mix well and set aside.
In a large stainless steel saucepan, combine vinegar, water, sugar and salt. Stir well and bring to a boil over medium-high heat. Reduce heat and boil gently for 5 minutes. Add asparagus and return to a boil. Boil for 2 minutes or until asparagus is heated through.
Place 1 (one) tablespoon of the chopped pepper misture, 1/2 teaspoon dill seeds and 1/2 teaspoon mustard seeds into each hot jar. Pack asparagus, tips down, into hot jars to within 1/2 to 3/4 inch from the tops of jars. Remove air bubbles and adjust headspace, if necessary, by adding hot pickling liquid.
Wipe rim. Center lid on jar. Screw band down until resistance is met, then increase to fingertip tight.
Place jars in canner, ensuring all are completely covered with water. Bring to a boil and process for 10 minutes. Remove canner lid. Wait 5 minutes, then remove jars, cool and store.