Place onions in a large glass or ceramic container; sprinkle with salt. Add water to cover. Cover and let stand in a cool place 12 hours. Drain and rinse onions several times in cold water.
Pack onions into 7 hot sterilized jars. Place 1 hot red pepper and 1 bay leaf in each jar.
Combine vinegar, sugar, mustard seeds, and horseradish in a stainless steel stockpot. Bring to a boil. Reduce heat; simmer 15 minutes, stirring occasionally. Pour syrup over onions, leaving 1/2-inch headspace. Remove air bubbles. Cover with metal lids, and screw bands tight. Process in boiling water bath 10 minutes.