It depends how much is on the bagel… and watch out for them pastries… “Poppy seed cake, bagels, muffins, and rolls did not contain sufficient quantities of poppy seeds to give rise to opiate positive specimens by U.S. Department of Defense (DOD) GC-MS cutoff levels (morphine = 4000 ng/mL, codeine = 2000 ng/mL), although a number of specimens were positive by National Institute on Drug Abuse (NIDA) cutoff levels (morphine and codeine = 300 ng/mL). However, ingestion of poppy seed streusel or Danish pastry led to confirmed morphine and codeine positive specimens, irrespective of the use of DOD or NIDA confirmation cutoff values.” Source: pubmed article