While it is well understood how to efficiently protect the data path in an asynchronous transmission channel against transient faults, much less is known about protecting the handshake signals along with their associated logic -- mostly a Muller Pipeline -- although these are equally critical for the proper function. In this paper we analyze the possible failure scenarios in the handshake of a 4-phase bundled data protocol that can arise from transient faults and systematically elaborate mitigation techniques for the resulting effects, namely single event transients and single event upsets. By simulated fault injection we show the effectiveness of the proposed extensions for protecting the channel. We take care to make these extensions themselves immune against transient faults, and we prove their proper and deadlock-free operation under fault conditions by means of model checking. Finally we show that, while providing superior coverage, our approach is in line with comparable approaches with respect to the area overhead.