Since this post is nearly a week old and no one has answered, I'll try. But, be advised that my last visit was a couple of years ago before construction of the mega-bridge began.

Once you cross the old bridge into Sunset Beach, I've been able to find limited free parking along the road before you get to Main St. Across Main is the fishing pier and a parking area. I seem to remember a charge there but that may be a seasonal or even day of the week thing. Bird Island is, of course, to the right. If you follow Main all the way to the end, I think there are one or two free spots at the end of the road. Probably already taken and not worth it if you have a bike.

The ride/walk is along the beach. Every time I've been, the beach has been wide and the sand hard near the surf. But, here in NC, the tides can change dramatically with moon phases, weather, and the season of the year. So, YMMV. Remember, it was an island separated from Sunset by an inlet at low tide not that many years ago.

Good luck!