Three and and a half months from Antalya to Bitlis. This was my longest bicycle tour in Turkey (my Erzurum to Bayburt tour was a couple weeks longer, but I spent a month of that in Georgia). By the end I was getting tired, but that’s more because Ferda didn’t allow us a rest day. She was anxious to get back to Antalya. With some rest I could have kept going to Nemrut, Ahlat, Van, and beyond.
You can take the main highway from Güroymak to Bitlis, but you can also choose the old road. It’s not well maintained, but most cars could get through, I think. There’s probably one problematic stream crossing. With bikes, it’s easy, of course.