Harbour Island is indeed the best choice, it's accessible on a day trip and via public transport, which is a rarity in the Bahamas -- for most other islands, if you're in any sort of hurry, the only sensible option is to fly.
Specifically, Bahamas Ferries has a daily fast ferry service that leaves Nassau at 8 AM and arrives at Harbour Island at 11 AM, returning at 3:40 PM for a 6:30 PM arrival back in Nassau (winter 2013 schedule here). At time of writing, the cost is $131 for an adult round-trip, or $190 for the "Dayaway" package including a tour of the island -- which you don't really need since it's a short half-mile from the dock to the pink sand beach.
And if $130 sounds expensive, well, welcome to the Bahamas; there are no other scheduled boats, a charter would be stupendously expensive (in the thousands if not more), and a round-trip flight to the nearest airport on Eleuthera would cost you >$150 and still leave you on the wrong island.
Last but not least, I know you're asking specifically for a pink sand beach, but the most stunning beach I've ever set my eyes on anywhere in the world -- and to calibrate that, I lived in South-East Asia for seven years and have been to places like the Maldives and Rarotonga, so I've seen a few in my time -- is Half Moon Cove on Saddleback Cay in the Exumas, which is also reachable by day trip from Nassau. The picture above doesn't do it justice, the whiteness of the sand is blinding and the color of the ocean is hallucinogenic. So unless you're really set on pink, do consider other options as well!