Would an epidural morphine show up in a drug screen?

Yes, but for how : Long. If you had drug screen the day after epidural, it may be positive. Half life of morphine is 2-3 hours and screening test is likely to be negative after 2-3 days, if that was the only use. Repeated use will give positive results for a longer period.

Drug screen: Really good question. Duramorph is morphine that is used in the epidural space. Typically a small amount is used (3-5mg), but it does distribute throughout the body. It is possible that a very sensitive drug screen could pick up morphing or its metabolites.