Estimating the effects of treatments with an associated dose on an instance's outcome, the "dose response", is relevant in a variety of domains, from healthcare to business, economics, and beyond. Such effects, also known as continuous-valued treatment effects, are typically estimated from observational data, which may be subject to dose selection bias. This means that the allocation of doses depends on pre-treatment covariates. Previous studies have shown that conventional machine learning approaches fail to learn accurate individual estimates of dose responses under the presence of dose selection bias. In this work, we propose CBRNet, a causal machine learning approach to estimate an individual dose response from observational data. CBRNet adopts the Neyman-Rubin potential outcome framework and extends the concept of balanced representation learning for overcoming selection bias to continuous-valued treatments. Our work is the first to apply representation balancing in a continuous-valued treatment setting. We evaluate our method on a newly proposed benchmark. Our experiments demonstrate CBRNet's ability to accurately learn treatment effects under selection bias and competitive performance with respect to other state-of-the-art methods.