If you want to do a camel trek from Agadez to Bilma you will most probably have to go in November or December and to follow the carawanes (salt). And this is really really hard work. You will walk/ride up to 10 hours a day at least!
But there are also possibilities for other camel treks in Niger, or organised tours with camel treks and small groups. I will do, for example, a 2-3 week trek in the Tamgak region (near Iferouane).
With such tours, you normally walk/ride 4-6 hours a day and you have more time to visit things on the way.
About Timbuktu I have no clue: never been there...