I believe Island Surf and Sail is open on Sundays in Soper's Hole. They have frozen bait available. You could probably get them to deliver something too for a minimum order, or for a fee, likely they will be delivering an assortment of water toys to customers around the island that day anyway.

http://www.bviwatertoys.com/fishing-tortola-bvi/

Also, the fuel dock/gas station in Cane Garden Bay has frozen squid available. Last time I asked the guy, he left and went to someone's freezer (in a nearby home I think) and brought me back two boxes.