Bidirectional Long Short-Term Memory (BLSTM) Recurrent Neural Networks (RNN) acoustic models have demonstrated superior performance over Deep feed-forward Neural Networks (DNN) models in speech recognition and many other tasks. Although, a lot of work has been reported on DNN model adaptation, very little has been done on BLSTM model adaptation. This work presents a systematic study on the adaptation of BLSTM acoustic models by means of learning affine transformations within the neural network on small amounts of unsupervised adaptation data. Through a series of experiments on two major speech recognition benchmarks (Switchboard and CHiME-4), we investigate the significance of the position of the transformation in a BLSTM Network using a separate transformation for the forward- and backward-direction. We observe that applying affine transformations result in consistent relative word error rate reductions ranging from 6% to 11% depending on the task and the degree of mismatch between training and test data.