I dont recommend that. Post edit action has many custom filters and actions binded to that, and if you will try to update post by a non-standard, custom method, then you may have some problems…
I advice to go to default EDIT page, (or in worst case, try some plugins, named i.e. “Front Edit” plugins or etc…)
If you still need the way you say, then you have to build custom <form> within front-end admin bar, that i think, will be hard for you.