"I want to be able to snap to the end of the text string so I can copy it uniformly and spaced evenly. Is there a command for this?"
There's no specific "command" for this, but you can certainly copy anything uniformly and evenly by snapping from any point you choose on the object as long as you select the same point consistently each time you copy. For a bubble callout (with a circle around it, as you say), the CENter or QUADrant snap should work just fine.
If you insist that it be the end of the text string, you would have to make sure the text string is justified bottom right (or "fit"), and use the INSert snap. Beware that text strings of differing lengths or characters (depending on font) may not give consistent results.
