In a large nonmetal bowl, combine squash, onion, and sweet pepper. Sprinkle salt over vegetables; stir gently to combine. Cover and chill in the refrigerator for 1 hour; drain well.
In a 3-quart stainless-steel, enamel, or nonstick heavy pot, combine sugar, vinegar, mustard seeds, celery seeds, and dry mustard. Bring to boiling, stirring until sugar dissolves. Add squash mixture. Return to boiling. Remove from heat.
Ladle hot vegetables and liquid into sterilized pint canning jars or other jars. Cool for 30 minutes. Seal and label.
Chill for at least 24 hours before serving. Store in the refrigerator for up to 1 month.