In my book secrets are worthless in a relationship - be open. If she doesn't like it, discuss her feelings on the matter in an adult manner.
Add your views - and remember, discuss, not argue.
If it looks as though it is going to create a problem asses the value of your relationship and whether the happiness of your current girlfriend is of more importance than meeting your ex. Sometimes you have to give a little.
Ultimately, if you are asking the question, it is clear you wish to have the platonic relationship with the old Doris, so why not just come clean - say what you feel - adding that you only have eyes for your current girlfriend.
Or - be a proper man, if you have nowt to hide, and take your current girlfriend with you.
I'm very much of the feeling honesty is the best policy - the truth usually comes out sooner or later, and if you've been keeping skeletons in your cupboard - it could backfire on you in a way you really don't want.
What's the worst that could happen?