13 But going ahead to the ship, we set sail for Assos, intending to take Paul aboard there, for so he had arranged, intending himself to go by land. 14 And when he met us at Assos, we took him on board and went to Mitylene. 15 And sailing from there we came the following day opposite Chios; the next day we touched at Samos; and  the day after that we went to Miletus. 16 For Paul had decided to sail past Ephesus, so that he might not have to spend time in Asia, for he was hastening to be at Jerusalem, if possible, on the day of Pentecost. (Acts 20:13-16 (ESV)
Pentecost was one of the major and required festivals of the Jewish faith. Jews were required to be in Jerusalem for this holiday, which is why there were so many on the day of Pentecost after the resurrection. I think we often forget that Pentecost was a Jewish festival. It was at festivals like this that a man would spend his tithe buying booze and meat. Perhaps also why people would accuse Peter of being drunk at nine in the morning. Today we read that as sort of an insult directed at the disciples, and though there might be some aspect of that in the accusation it would not have been so weighty an insult as it is today. These holidays were meant to be celebrated and moderate inebriation was pretty much expected to be part of that celebration.
This would also be a time that people who had taken a Nazaretic vow would complete that vow in the temple, and resume life as normal. It seems this is something Paul is anxious to do. He bypasses Ephesus. I find this a little funny. He loves the Ephesians, and the Ephesians love him. He knows if he stops, he won’t be able to resist their hospitality and he will be stuck there for quite some time. So he doesn’t even bother to stop. There will be time enough for him to return later, at least so is his thought.
Obviously the Ephesians would know as would others, when reports come of Paul in Jerusalem that he had skipped by them. It would be natural for them to feel a little slighted by this. I hate it when I have opportunity to be in the local vicinity of old friends and yet don’t have time to visit with them. It’s also a bit of a letdown when you realize friends have passed through and didn’t have time to drop in. But life is like that. Sometimes there just isn’t time. Luke feels it necessary to explain why Paul passes Ephesus, there is a note of apology in the explanation. In its own way it is a testimony to Ephesian hospitality.