I just bought the bag for the city mini for our upcoming trip. I tried it out, and while it will certainly protect the stroller, its a bit cumbersome to deal with. I had to lay the bag open on the floor, take all the wheels off, stow them just right in the pockets of the bag, then lay the stroller on top. It is not something I would be able to do right at the plane door (it would have to be done while still at the gate in the terminal).
Last time we flew, we gate checked our stroller (not the mini, a different one) in its bag. We saw the baggage handlers haul about 5 or 6 umbrella strollers all stacked on top of each other up from the plane and basically dump them in a pile outside the plane door. Then, the guy came back with just our stroller bag, holding it by the handle, and gave it right to us. He appreciated that it was in a bag since it was so much easier to hold.
For flying alone with a little baby, I probably wouldn't use the bag. I would still be concerned about the stroller getting dirty or damaged though. Do you have another stroller that might be easier to handle (and don't mind risking damage) like a cheap umbrella stroller or a frame stroller for an infant seat?