Hi Kostas & welcome!
Three years ago I started my first Turkey trip also via Chios and Cesme, travelling more or less on your route, but continuing to Ephesos and further east, right to the Iranian border.
I found the western region very similar to the Greek back-country. Quite civilised  compared to the far east - at least concerning the roads and herd dogs. I travelled on an old Beemer, usually going between 60 - 90 kph and never felt too slow for the traffic around. Istanbul is a different story....
So IMHO your 125cc bike should be ok. On the motorways the speed limit for bikes (even big bikes) is restricted to 80 anyway.
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Only when we pause to wonder
do we go beyond the limits of our little lives.
(Rod McKuen)
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