Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of important nonlinear dynamic features such as backbone and nonlinear frequency response curves. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically-coupled modes. The regression model is also exploited to estimate the uncertainty of the identified features.