As a business owner, I travel away from home for a couple of days at a time on a regular basis. Am I allowed to collect the per Diem listed in pub 1542 for my overnight travel, or can I collect only if I have travel expenses backed up by receipts?

You can use the per diem amounts for Meal and Incidental Expenses, but the lodging costs must be what you actually spent on lodging as documented by receipts.