Despite the advent of touchscreens, typing on physical keyboards remains most efficient for entering text, because users can leverage all fingers across a full-size keyboard for convenient typing. As users increasingly type on the go, text input on mobile and wearable devices has had to compromise on full-size typing. In this paper, we present TapType, a mobile text entry system for full-size typing on passive surfaces--without an actual keyboard. From the inertial sensors inside a band on either wrist, TapType decodes and relates surface taps to a traditional QWERTY keyboard layout. The key novelty of our method is to predict the most likely character sequences by fusing the finger probabilities from our Bayesian neural network classifier with the characters' prior probabilities from an n-gram language model. In our online evaluation, participants on average typed 19 words per minute with a character error rate of 0.6% after 30 minutes of training. Expert typists thereby consistently achieved more than 25 WPM at a similar error rate. We demonstrate applications of TapType in mobile use around smartphones and tablets, as a complement to interaction in situated Mixed Reality outside visual control, and as an eyes-free mobile text input method using an audio feedback-only interface.