Our RS tour ends Oct 1 and I noticed there is another RS tour ending on Oct 3. Can we take the bus to Izmir on the 3rd?
I can't imagine why not. The bus won't be full. Just ask your guide and I'm sure they will confirm it.
Worst case, the hotel will be able to arrange a car for you.
I would also make sure to have your guide give you the name and phone number of the following tour's guide so you can connect with them for any last minute changes in arrangements (especially if they're not staying in the same hotel as your tour). The departure time to the Izmir airport depends on the actual flight times for the tour group members so you'd need to know when they plan to leave (there is no set time for that shuttle service).