You're quite right. Both to talk and talking are possible, valid options here. Good catch.
Edit: About the difference in meaning, I think it boils down to the difference between two meanings of to try. This is something I'm quite aware of because each gets expressed with a different word in my other primary language, Spanish.
try = probar: try something out. Try (gerund). Here one's approach is experimental. You give something a try, and maybe it works, maybe it doesn't. That is what is meant by try talking to her. Maybe the two of you will reach a solution together. Another example:
"What should I say to the judge?"
"Try telling the truth. He may be impressed with your honesty."
try to = intentar: attempt. Try (infinitive). Here, we don't know if she will be willing to talk to us. The sentence says, "Attempt to talk to her." But maybe she'll refuse to talk at all. Another example:
"Try to relax. Remember, all you need to get on this test is a passing grade, which is a 65%."