It's always a bit nerve racking if you haven't done it before! I was on the same cruise as
@PurplePencil and it was a disaster with immigration BUT as has pointed out, we had immigration because of our itinerary-BCN to BCN shouldn't have that.
The airport can be calm or totally chaotic depending on the ebb and flow of tourists, especially cruisers. The lines to drop off bags were crazy (and we were there 3 hours before the flight, right as they were opening up the bag drop off). Security wasn't better (again, this is timing) and then there is a border control check before the gate and
after most good shopping/eating (although I have the taste buds of a 5 year old and really enjoyed McDonald's bruschetta!).
DCL had buses waiting to fill then leave the port so if you take DCL transport then I'd do walk off and get on the bus. Other options are private transport and cabs (which appeared to be plentiful when we disembarked around 7:45 ish).
Of course there are no guarantees but I'd think that if you did walk off and got on the first bus or took a taxi and there wasn't bad traffic then 11:15 should be do-able (if not a wee bit stressful). I hate stress so rats, am staying an extra 2 nights in Barcelona after our upcoming cruise (any excuse...).