  In this paper, using Klyachko's classification theorem we study positivity
and semi-stability of toric vector bundles on a class of nonsingular projective
toric varieties, known as Bott towers. In particular, we give a criterion of
$s$-jet ampleness of line bundles and characterize nef and big line bundles on
Bott towers using Bott numbers. We obtain a criterion for the ampleness of
discriminant zero semi-stable toric vector bundles on nonsingular projective
varieties. We also describe toric subbundles of toric vector bundles on
nonsingular toric varieties.
