Never used Greyhound. Since you're both near Forward Air terminals, look into that. With Forward Air, the shipper drops the package off at their local terminal and you pick it up at yours. Don't let the name fool you, it goes buy truck but LA to Nashville would only take 3 or 4 days...
I've used them a number of times...a couple Acoustic folded horns to Cleveland and Florida and an Ampeg 8x10 to San Francisco. Excellent experiences all three times. In 2002, it cost something like $45 to ship the Ampeg from Chicago to San Francisco...darn cheap!!!
http://www.forwardair.com