Plus at Grande Ocean they will give you a Bike Sea Pines pass which they usually won't (though sometimes will) if you don't rent from them. We've rented from Marriott and off site, going forward we'll likely rent from Marriott due to the convenience but off site worked well also and in some cases, had better bikes.
Correct and it's a separate pass from the car pass so just buying a car pass won't get you in with bikes unless you take them in by car. From Barony it's not likely an issue as most aren't going to go that far then explore Sea Pines but some avid bikers might. Also, based on past experience, MGO only gets so many passes so even renting from them midweek you might not get one. I've seen them give passes out even if you didn't rent from them, esp if you bring your own bikes, but they made it clear this was something they did on a limited basis. I do not know if other Marriotts give a bike pass but I would not be surprised if those inside sea pines do and the rest do not.
Several posters have already offered helpful information regarding bike riding on Hilton Head Island. Bike rentals on Hilton Head Island are beach cruisers. I hesitated to post because you already have your reservation at Barony which is about 9 miles from the Sea Pines Ocean gate. That is a long ride sitting on the wide saddles of beach cruises. On one trip, we rode beach cruisers with backpacks from the airport to Monarch..and back to the airport. (We decided afterwards that the experience is one we could have not done and still had a full and rewarding life.) As others have said, you can’t get a bike inside Sea Pines unless you are staying at Grande Ocean or within Sea Pines. Staying at Barony or any ocean front Marriott on Hilton Head Island, you will have fantastic hard pack sand to ride on the beach. The paved bike path from Barony runs along highway 278 which is not a very interesting bike ride. If you like to bike ride, you are very likely to enjoy the bike paths in Sea Pines. You can experience Sea Pines bike paths by paying the $8 entry day fee and renting bikes for a day. The scenery along the paths, the Sea Pines Forest Preserve, Lawton Stables, the community garden plots and the tourist stops of Harbor Town and South Beach are all within riding distance once you are inside Sea Pines. Our first vacations to Hilton Head Island were outside Sea Pines. The other Marriott resorts on Hilton Head Island have their strengths and are favorites for many, but Sea Pines is the reason we go to Hilton Head. For the beach and ocean, bike riding and our other interests, Monarch (in Sea Pines) and Grande Ocean (car and bike passes into Sea Pines) are special.