I know I'm a little late to this party but I was having the same problem and came across a solution that solved it. In case anyone else is having the same problem and finds this question doing a search here is the answer:
Add the class "clickable" to whatever you're tapping on with your iOS device that's supposed to open the modal. I assume you're using a div because an a tag or button should work just fine. Then in your CSS put this:
.clickable {
cursor:pointer;
}
This is not a Bootstrap problem, it's an iOS problem. The pointer lets iOS know that whatever you're tapping on is clickable, which normally doesn't include a div.
I won't take credit for this answer, I found it here:
Bootstrap Modal does not work on iOS devices