Bulguksa and Seokguram can fit into one car-free day, but the uphill connection sets the pace. Start with the temple you most want to see and treat the second visit as dependent on the next bus.
Reach Bulguksa first
Gyeongju City lists bus 10 between the terminal area, historic centre and Bulguksa; its route page gives a terminal-origin first bus at 06:00, last at 21:40 and an approximate 20-minute interval. Check the city bus route details for your travel date.
Check the Seokguram connection before leaving the temple
VisitKorea describes a roughly 20-minute shuttle from Bulguksa, with departures about once an hour. Seokguram is also 3 km away by hiking trail and 9 km by road; that distance is not a quick walk between sites. Confirm the next outbound and return services before committing to both. See the Bulguksa–Seokguram visitor guide.
Protect time at the site, not just the transfer
Visitor listings give both sites daytime hours, around 09:00–18:00; Seokguram's listing allows viewing until 19:00. If the service gap leaves little time for either grounds, stay with Bulguksa and return to town. For the broader local bus plan, see Gyeongju without a car.