Hi Kim. My husband seems to recall that the taxi fare was around 25 Euro (same as Cruise Fanatic stated) from hotel to ship. We stayed outside the Las Ramblas area, though, at Diagonal Mar, yet I don't think there would be much of a difference. Definitely skip the shuttle. Also consider skipping it on the way from ship to airport... transfers purchased on the ship were $30 per person, while we paid 35 Euro total (equivalent to $45 at the time) for three people via taxi.
I just remembered something important for ALL pax planning excursions with independent companies. We stayed on ship's time throughout the cruise.