Type-0B string theory has been proposed as the dual description of non-supersymmetric SU(N) Yang-Mills theory coupled to six scalars, in four dimensions. We study numerically and analytically the equations of motion of type-0B gravity and we find RG trajectories of the dual theory that flow from an asymptotically free UV regime to a confining IR regime. In the UV we find a one-parameter family of solutions that approach asymptotically AdS₅ × S⁵ with a logarithmic flow of the coupling plus non-perturbative terms that correctly reproduce all UV and IR renormalon singularities. The first UV renormalon gives a contribution ∼ F₁(E)/E² and we are able to predict also the form of the function F₁(E), which, from the YM side, corresponds to summing all multiple-chain bubble graphs. The fact that the positions of the renormalon singularities in the Borel plane come out correctly is a non-trivial test of the conjectured duality.