Let G be a finitely generated group that can be written as an extensionwhere K is a finitely generated group. By a study of the BNS invariants we prove that if b 1 (G) > b 1 (Γ) > 0, then G algebraically fibers, i.e. admits an epimorphism to Z with finitely generated kernel. An interesting case of this occurrence is when G is the fundamental group of a surface bundle over a surface F ֒→ X → B with Albanese dimension a(X) = 2. As an application, we show that if X has virtual Albanese dimension va(X) = 2 and base and fiber have genus greater that 1, G is noncoherent. This answers for a broad class of bundles a question of J. Hillman ([Hil15, Question 11(4)]).