The usual version of collection is the second one in Kaveh's answer. It, with the remaining axioms, won't give the axiom of union. A counterexample is given in the question, except for a slightly unusual definition of $H_\kappa$ for singular $\kappa$; it should be the collection of those sets $x$ such that each member of the transitive closure $TC(\{x\})$ has cardinality $<\kappa$. (This does not imply that the whole $TC(\{x\})$ has cardinality $<\kappa$, which is the usual meaning of $H_\kappa$.)
The "appropriate version" of collection used by Bourbaki seems appropriate mainly in the sense that the axiom of union has been built in.
