This work introduces a new problem in the field of multi-fidelity Bayesian Optimisation: optimising black-box functions when multiple correlated information sources can be sampled, and the cost associated with sampling is dynamic - changing based on the distance (in the sample space) to the most recently sampled point. This new feature of the problem - a dynamic cost function - aims to recreate a practical issue which is commonly seen across a multitude of different engineering applications. Often, when attempting to optimise some objective function using multiple information sources with various associated costs and biases in sampling, there is, in practice, a cost associated with switching between information sources, as well as between different points in the design space. For example, there may be large time and resource implications associated with adjusting multiple parameters of a lab experiment by a large amount, rather than making small adjustments to a single experimental parameter. Furthermore, the cost of changing these parameters is reduced in specific dimensions when observations already exist for those dimensional values. In previous work, only the cost of the experiment itself has been considered, and these (possibly substantial) transition costs are neglected entirely. In this work, this new aspect is introduced, and the resulting consequences for multi-information source Bayesian Optimisation algorithms are explored on a series of synthetic test cases and then applied to a relevant aerospace engineering case.