The Old Buccaneer in question happens to be Billy Bones, who rocks up one fateful day at the Admiral Benbow inn with a mysterious sea chest in tow. Upon arriving, this colorful character proceeds to take over the place, getting drunk on a daily basis and terrorizing the customers, not to mention the landlord, Jim Hawkins's father.
At the same time, however, it becomes clear that there's more to this salty old sea-dog than meets the eye. Beneath his rough, bluff exterior there beats the heart of a vulnerable man who senses that he doesn't have long to live. Billy Bones may appear to be the quintessential tough guy, but in actual fact, he's scared stiff. Why? Because he knows that his former shipmates, all pirates, cutthroats, and thieves like himself, are hot on his trail. He's got something—the treasure map, no less—which they think rightfully belongs to them, and they're prepared to do anything to get their greedy hands on it.
So Billy Bones has every reason to be afraid. He's "nervous and scared" because he knows full well what his former colleagues are capable of. It's notable that Billy Bones suffers a stroke not long after he sends the villainous Black Dog packing from the inn. Though he fought bravely in their brief but bloody duel, Billy Bones still has every reason to be scared of Black Dog and those who will certainly come after him to look for the treasure map. Even if alcohol abuse was a contributory factor to his stroke, there seems little doubt that fright also had its part to play.