We traveled quite a bit when my son and daughter were potty-training. We'd bring pull-ups for nighttime, and I carried extra shorts and undies in my purse for any accidents. The key for us was making sure we took them to the bathroom several times a day and had them try to "go," so we could stave off accidents. (They were so distracted by all the sights, they'd forget to listen to their natural cues that it was time to use the bathroom.) It took some extra time, but certainly no more time than it would have taken to change diapers/pull-ups, and they were so proud that they could do it on their own.