This morning I rode home from REI with my new 'cross bike. However, I also rode home with (on) my touring bike that I had ridden to REI. I found that while riding carefully down the street steering the bike I was riding with one hand and the new bike with another, motorists went much farther around me than normal. I'd done this before, and the only really hard thing is steering the bike you aren't riding (note: unweighted bikes being steered by the stem are very twitchy ) and cornering. I also got a lot of friendly comments along the lines of "Looks like you lost a rider there" including from the nice elderly women who always stand at this one street corner holding a sign with a picture of a mutilated fetus.

So anyways, if you want visibiity, ride two bikes to work.