Ample vector bundles with zero loci having a bielliptic curve section of low degree

Let E be an ample vector bundle of rank r \geq 2 on a smooth complex projective variety X of dimension n such that there exists a global section of E whose zero locus Z is a smooth subvariety of dimension n-r \geq 3 of X. Let H be an ample line bundle on X such that its restriction H_Z to Z is very ample. Triplets (X,E,H) are classified under the assumption that (Z,H_Z) has a smooth bielliptic curve section of genus \geq 3 with H^{n-r}c_r(E) \leq 8.