I did it…!
I rode my new bike the seven miles into work this morning. And I did it in 40 minutes.
My legs are tired, but not nearly as tired as my back is (I carried a messenger bag with all the necessary stuff [first aid kit, wallet, dress shoes, rain poncho, etc] in it today). I think I will have to invest in a rear bike rack (one of those that hooks onto the seat-post, over the rear tire) and a set of those saddle-bag style thingys that the cross-country bicyclists have.
But! Forty minutes over seven miles for someone who is really out of shape is not too shabby.
The crazy thing is, now I get to do it again on my way back home…!