Minibuses run between Selçuk's otogar (bus station) and Şirince every 30 minutes during the warm months (April through October), more frequently (about every 20 minutes) on busy summer weekends, less frequently in the winter (November through mid-March). Ask about the time of the last minibus when you arrive at Selçuk's otogar, or in Şirince.
If you plan to use Şirince as your base for several days of exploration in the region around Ephesus, you should consider renting a car. Having your own car makes it easier to travel from, and return to İzmir's Adnan Menderes Airport, to make day-excursion trips to Priene, Miletus and Didyma; Euromos and Bodrum; Aphrodisias, and even Pamukkale.
For a day-trip to İzmir, however, I recommend taking the train to İzmir's Basmane Gar. Park your car near the gar(train station) in Selçuk and take one of the half-dozen daily trains, or drive north to Cumaovası, from which you can take any of the far more frequent İZBAN suburban trains directly to Basmane.
By taking the train you save yourself the considerable hassle of dealing with İzmir's frantic traffic and driving, and impossible parking..
—by Tom Brosnahan.