Confidence estimation for automatic speech recognition has been very recently improved by using Recurrent Neural Networks (RNNs), and also by speaker adaptation (on the basis of Conditional Random Fields). In this work, we explore how to obtain further improvements by combining RNNs and speaker adaptation. In particular, we explore different speaker-dependent and -independent data representations for Bidirectional Long Short Term Memory RNNs of various topologies. Empirical tests are reported on the LibriSpeech dataset showing that the best results are achieved by the proposed combination of RNNs and speaker adaptation.