Larger mature dolphin are an interesting fish. They can be very picky. One taste of plastic, and they are history. The large bulls have a fairly good size mouth and can take a large bait. Flying fish are always found in the stomachs of the large fish when I clean them. That's why I like to use a bait or artificial that skips the surface when working a weedline or rip.
It's very frustrating to have a big bull in the spread of lures and see him running in-between them and go away. This is where being prepared will pay off. You only have 30 seconds or less to toss them a rigged strip bait (Bonita belly) or ballyhoo. I try to keep a rigged natural bait in the bait box rigged and ready with a casting rod readily available in a near by rod holder.
If the dead rigged bait isn't eaten, try tossing out a live bait. The best bait by far would be a live flying fish, but that's almost impossible to achieve. All of the above is pertaining to large solitaire fish. (35lbs and up)
I agree with Bigmike on the chrome jet head with feathers. Average size dolphins (10 to 25 lbs) love feathers. I prefer a light weight chrome head that will stay on top and fish them off the outriggers. They also love a skirted ballyhoo. If I only had one natural bait on board for dolphin it would be the ballyhoo.
Dolphin are bleeders. The biggest clean up on a boat is after a good dolphin bite. Just the hook removal will make your boat look like you have sprayed blood all over with a spray gun. Try to get them in the box ASAP. Catching chicken size ones can be very bloody. Letting them bounce around the deck while getting hooked up again and again is a nightmare of mopping up blood.
Dolphin are great fighters and put on a great acrobatic show. They also are great table fare. Not catching one during a day of trolling is disappointing. It's always a good day to have a couple of medium to large size dolphins in the box.