Editor's English translation below:

Uludağ summit route is available in the wikiloc program.
As long as you are not leaving the alpine region, you do not need a guide.
You may need to pay attention to the weather in October.
Because the weather gets harsher quickly in Uludağ.
If you notice the barometer falling rapidly, you should get off the mountain.
From the hotel area, the peak takes at least 3 hours to reach. In October there is probably no snow.

You can buy the cable car tickets from the cable car booth.
bursateleferik.com.tr/fiyat-tarifesi/
If you go to the mountain on the weekend, you can wait for a little ticket queue up and down.
but if you go early you will get on the cable car early.

There are also minibuses to Uludag from Tophane district.
When the minibus is full, it goes up. It's not scheduled.
Think of it like like a charter.
This answer is late for you, but maybe you too could delay the climb.
Have fun.