How do I widen an existing asphalt driveway with crushed gravel?
3/4 minus (21AA in US Midwest) is perfect for this
application.

Hope you have some college kids around, that's nearly 2 cubic yards!

I would overdig another 6" to be able to place an edging to retain the gravel and make a clean edge.

Place the gravel in 2" "lifts" (lay down 2") and then compact with a plate vibrator.  Repeat twice. Enjoy! 

6"  compacted will be quite solid and stable. 

Update

This edging can be backfilled with dirt to grow grass.  Just place it when you are 2 1/2" from the top.  Its usually staked with landscape nails every 2 ft, but I'd do it every foot.  I know you're not using pavers, but this will retain the edge of the gravel.  You don't have to do anything with the asphalt edge, unless it is rolled over unevenly, in which case you can cut it with a masonary blade in a circular saw.