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This paper proposes a nonparametric approach to estimating the dependence relationships between circular variables and other circular or linear variables using copulas. The proposed method is based on the use of Bernstein copulas which are a very flexible class of non-parametric copulas which allows for the approximation of any kind of dependence structure, including non symmetric relationships. In particular, we present a simple procedure to adapt Bernstein copulas to the circular framework and guarantee that the constructed bivariate distributions are strictly continuous. We provide two illustrative case studies, the first on the relation between wind direction and quantity of rainfall in the North of Spain and the second on the dependence between the wind directions in two nearby buoys at the Atlantic ocean.