An obvious answer to the above question is that what Turkey wants is an official partition and the recognition of two separate states in Cyprus and that a "BBF" kind of solution is a compromise for them.
It seems that this is not the case. A "solution" of the type of Annan plan is the ideal (not a compromise) "solution" for Turkey. For the Turks an Annan plan kind of "solution" is not only far better than the status quo, it is actually the ideal "solution" even better than a two state "solution".
Why is this the case? Because Turkey wants to control the whole of Cyprus, not just a 3rd of it. The recent claims by Turkey that Turkish Cypriots & Settlers (i.e. their proxy) should have a say about any natural gas finds in the sea south of Cyprus is a testament to this. Turkey wants to turn the whole of Cyprus into a Banana Republic controlled by themselves, just like the pseudo state in the north is today.
On the other hand with a two state "solution" Turkey would have to abandon all claims over the south part of Cyprus and over the sea south of the island, something which wouldn't go well with their plans to dominate the whole region.
Thankfully the majority of the Cypriot people were smart enough to reject the Anan plan which would have destroyed Cyprus. 2/3rds of our island are still free and we still have the ability to continue fighting for the liberation of the remaining third, something which can not possibly come with negotiations at the height of the Turkish power, but in the right time under a different balance of power.