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 to appropriate mainly in the sense that the axiom of union has been built in.

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.