We obtain a lower and an upper bound for the 2-Wasserstein distance between self-similar measures associated to two increasing non-overlapping linear contractions of the unit interval. We use a method of approximation of the measures via iterations of the Hutchinson operator on a delta Dirac measure. This allows us to obtain explicit estimates for the 2-Wasserstein distance between the approximating measures. We use these bounds to obtain the bounds for the distance between the self-similar measures.