By asking her out to dinner, it opens you up to rejection. It lets her know that you're still interested and the more interested you are, the more she will take that for granted.
It lets her know that you're not 'over' her.
It is persual.
If she DID take you up on your invite and then things progressed, she could backtrack and say it was all your fault because you initiated dinner.
(Andy has said to me before 'it's your fault because if you didn't keep being nice to me I could keep away')!
Or she could say 'you knew I divorced you and we're just friends, it's your fault for reading too much into it.'
Whenever I initiated anything at all, it backfired on me.
As lost said, her H was more interested if she DIDN'T ask.
Let your W do the running. She divorced you, it's up to her.