There are two ways to do that. I think GraphBuilder and RowState markers would be the easiest. First set the markers for the groups:
Circle and Triangle markers
Set up GraphBuilder
You can change the jitter option if you don't want the overlapping symbols dodging each other.
Or you can do it with BubblePlot the way you were trying by using Edit->Copy Frame Content and Edit->Paste Frame Content:
Use Draw and Shape to make the hollow shapes.
Copy the content from one...
...paste to the other.
I do not like the copy-paste choice because it would be an extra step, hard to script, leaves an extra graph on the screen, and the pasted points in the destination graph are NOT selectable. I think the GraphBuilder choice is much better.
Craige