Have you even considered telling her what your hesitation is? Nothing like just expressing feelings and concerns with the other person.
She might agree, that you have valid issues and indicate that she isn't ready to sever all ties with her ex. Or she might just be able to quiet those concerns by letting you know that while they have no intentions of ever becoming involved again, they are just friends. Or she might just tell you it is none of your business.
At least you would have more information to base your decision on, as how you wish to proceed with your friendship/relationship with this woman.
If she is showing an interest in spending more time with you, but you have been hesitant to do so, she may be wondering "What is wrong with me" which you could clear up with a talk with her.
If you two decide to take it to the next level, proceed slowly. One of the best tools at your disposal is conversations of what you are thinking and feeling. Don't expect her to know what you are feeling, tell her. Also encourage her to share with you, so you don't have to guess or make a misstep because you guessed wrong.
Lack of communication was a factor in the breakdown of my former marriage. I when I started dating again and met the man I married 2 years ago, I let him know that if he couldn't talk about things, that our relationship was not going to advance beyond freindship. He just chuckled and said "Great, because I feel the same way."
Talk things over with her. Let her know that you are interested and why you have been hesitant to presue that interest.