We consider onset of transport (de-pinning) in one-dimensional bosonic chains with a repulsive boson?boson interaction that decays exponentially on large length-scales. Our study is relevant for (i) de-pinning of Cooper-pairs in Josephson junction arrays; (ii) de-pinning of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunneling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped onto an effective model of a one-dimensional elastic field in a disordered potential. The standard de-pinning theories address infinitely long systems in two limiting cases: (a) of uncorrelated disorder (zero correlation length); (b) of long range power-law correlated disorder (infinite correlation length). In this paper we study numerically chains of finite length in the intermediate case of long but finite disorder correlation length. This regime is of relevance for, e.g., the experimental systems mentioned above. We study the interplay of three length scales: the system length, the interaction range, the correlation length of disorder. ... mehrIn particular, we observe the crossover between the solitonic onset of transport in arrays shorter than the disorder correlation length to onset of transport by de-pinning for longer arrays.