I think the present participle in this context would mean that she heard something as she was coming out from the bushes. The infinitive doesn't have this ambiguity. Therefore I would recommend the infinitive.

Thank you Chris, that's helpful.

But if she were coming out of the bushes, wouldn't it be "en venant"? If it's just "venant", it must apply to the nearest noun, I think, so there is no ambiguity.

According to the following discussion, it's a question of emphasis. 

https://french.stackexchange.com/questions/6285/infinitive-or-present-participle-in-a-sentences-object

I think, Alan, you raise a valid point. En venant would be wrong (i.e., it would mean that she was coming out of the bushes). Using only venant would most likely be in reference to the noise. But, to my ears, it still carries a bit of ambiguity which the infinitive doesn't.

Do you think the original text: "she heard a little squeal coming from the bushes" is ambiguous? Should it have been phrased "she heard a little squeal come from the bushes" to avoid that? In my opinion it's not, and I doubt that it's any more ambiguous in French.

I do think that the use of the infinitive is more common/idiomatic in French, but that may be related to the explanation given in the thread. Maybe it's normally the action that you want to put the focus on.

I've seen too many dangling participles in English. It is, of course, bad English but if there is a way to word something unambiguously I usually go with that. Therefore, I would also prefer "come" in English over "coming". It just removes any lingering doubt.