HELP I NEED ADVICE

So I’ve just started dating someone who’s recently come out of a long term relationship, she describes them as being on and off all the time and that they always ended up getting back together. I’ve told her that that scares me and shes just been quiet and weird with her answers. We’ve both seen each other loads and we get on so well and have both expressed we like each other. I’m just worried her past with her ex is going to get in the way and I don’t know how to act or behave as I don’t want to push her away if I get too paranoid. If anyone’s been in a similar situation please give me advice on what I should do😫😫