What are the historical roots of Milner's bigraphs?
Much of the category theoretic groundwork for bigraphs was done in terms of Reactive Systems:

Leifer, J. J. and Milner, R. (2000). Deriving bisimulation congruences for reactive systems. In Palamidessi, C., editor, Proceedings of the 11th International Conference on Concurrency Theory (CONCUR'00), volume 1877 of Lecture Notes in Computer Science, pages 243-258. Springer-Verlag. (link)

This was the result that showed that bisimulation is a congruence in the presence of sufficient RPOs.

As you correctly noted, there are definitely links with various ambient calculi - particularly in capturing the notion of "place".

The Chemical Abstract Machine (Cham) has also been cited as significant - probably in terms of the semantics of reactions as well as a few other concepts (such as membranes) that look familiar when viewed from the bigraphs world.  This to me probably shows the clearest sign of being an ideological ancestor of bigraphical reactive systems in many ways.

Finally, I think it's worth just looking at the thread of Milner's work from CCS, to pi-calculus, to reactive systems, to bigraphs.  You see a definite trend within that strand of work, in the introduction of additional abstractions or the ability to explicitly encode certain information that was perhaps otherwise only implicitly included in previous modeling formalisms.

This is by no means complete, but I think it's definitely fair to see the development of bigraphs as a natural progression from many, many different ideas.