Seems to me regardless of what you use, if you're concerned about harshness, it's really a question of dilution and method of application, and I have to imagine dish detergent is relatively mild to begin with. You'd think car and bike wash products would be relatively cheap by comparison, since they don't have to worry about purity, toxicity, or whether the residue is palatable.

Speaking of palatable, I got some Finish Line Super Bike Wash a while back, but it smells atrocious, so I just use Ajax dish detergent instead. And I often finish the job by wiping the bike down with a cloth sprayed with Pledge or store brand equivalent.