Was bombe machine turing complete?
No, the bombe was very specific. It consisted of a bunch of enigma machines hooked together. It was very limited in its use. A more interesting question is whether the Colossus computer, also used in Bletchely Park, was Turing-complete.

When asking such a question, it should be understood that no physical computer is Turing-complete, since it cannot handle arbitrarily large inputs. But even if we abstract this issue away (in any reasonable way), bombes are not Turing-complete. It could be fun to come up with an appropriate model and determine the exact complexity class covered by bombes.