I think you have not set the page permission correctly.
Just go to the sitemap. Click on the page where you want that user to make edit.
Click on set permission. Who can view this page? check your created group and Who can edit this page? check your created group. Click on save.
Now if the any user of that group login he can viw thae edit bar in the page where he has edit permission

Thanks for the response. I tried what you said. When I logged back in under her username, I was able to edit everything on the page. I only want her to be able to edit certain areas on the page. I have set permissions on the block that she is to edit but when I login under her name, there is no way to edit that particular block.

I have opened the page under my admin login. Clicked on Edit the page. Clicked on the block I want her to edit. Selected Set Permissions. Selected Edit Block. Added the group she is member of to those authorized to edit the block. Saved everything. Her group appears as having permission along with Admin to edit the block.

Hi,
Login to admin panel.
Click on Dashboard->Block & Stack Permission.
Then click on Add Block after that click on the plus icon of Access section.
After that select Group from the Select dropdown.
Select the usergroup for which you want to set permission.
Click on Save after that click on Save button of 'Add Block' popup and then click on Save button of Block & Stack Permissions.

Tried your solution but still having the problem. See my reply to Pluto.