You got the bike! That is half the battle right there. I am afficionado of steel frames and singlespeed bikes myself, so I am pretty keen on that Bianchi San Jose you got.

I too wouldn't worry too much about the mounting and dismounting part yet. You will see others who are not smooth or quick with that at a race, and it's not a huge deal. Get off and on as best you can as you feel comfortable. I learned the dismount from reading instructions online. I learned the mount from watching people do it.

Now, about a singlespeed. I ride a singlespeed mountain bike sometimes, and a singlespeed commuter a lot, and I have to say, sister, it ain't always easy. I do singlespeed for fun, but I don't do singlespeed when I race 'cross. Riding singlespeed requires quite an effort. A possible advantage in 'cross would be that you'll probably pass your competitors on the uphills, as they downshift. At any rate, you'll have the coolest bike in the race!