Just like most relationship issues, the best course of action is to clearly and non-violently communicate your desires – that you need more time to resolve your issues around your breakup, and would appreciate the time/space required to do so.
You're not telling her to jump off a bridge, just that by trying to "force" a smooth friendly post-breakup relationship isn't working for you. It's possible, or even likely, that you'd be open to such interaction in the future, but in order to get there, you need her to focus on her other relationships and responsibilities for the time being.
Now, asking for space is not the same as having your request honored. If she's unable to respect your point of view, then you will need to more actively cut her out of your life, even if that means taking various "anti-stalking" measures (new phone number/email/address if necessary). It really depends on the severity of the issue… I'd err on the side of caution and protecting your own emotional health, especially as the "dumpee".
Still, in most cases, a genuine and heartfelt request for space will be appreciated and observed. You may even score a few attraction points with someone else viewing from the sidelines – Handling a breakup well is a sign of high emotional intelligence, and women tend to like that in a partner.