There is no way to do this at the moment. Manipulating the event div wouldn't be too safe anyway, you would have to clear the changes after the bubble is dismissed and this would require quite a piece of code.
You could try a workaround by supplying your own JavaScript object as the bubble but it doesn't get any information about the source div. Such an object would have to implement showEvent(calendarId, eventObject) method. The bubble is cleared using DayPilotBubble.hideActive(); call. You would have to override this "static" method as well.
However, this seems to be relevant requirement. I would like to add an "arrow" to the bubble pointing to the event source in one of the future versions.