This is an example of Conversational Deletion, which I'm familiar with largely through John Lawler's explanations on ELU: here, for instance, and here. You can search ELU for more.
The basic idea is that in spoken English, people ordinarily chop unnecessary bits off the front of a sentence: the pieces that are entirely superfluous in conversation, because hearers can supply them from context. In your example, for instance, the bracketed words are deleted:
[It was a] bit of a nasty shock for him.
This doesn't work so well in written English, where sentences must be conventionally complete. But modern playwrights have employed it to extraordinary effect, looking to the actors to provide the depth of internal and external context which is deliberately omitted from the printed page. Reading Samuel Beckett, Sam Shepard and especially the early works of Harold Pinter will teach you far more about the natural construction and rhythm of spoken English (not to mention its unexpected capacity for lyric expressiveness) than a lifetime of listening to BBC broadcasts.