By the GAGA principle we know that a holomorphic vector bundle E->X is analitically isomorphic to an algebraic one, say F->X, and by definition F is locally trivial in the Zariski topology. But since the isomorphism between E and F is analytic, I fail to see if this implies that E is Zariski locally trivial too.

I hope the answer is not "trivially yes" for some stupid reason, but I cannot guarantee that.