Question: What castle in Ireland once occupied by the MacDonnells is accessible by a bridge?

Context paragraphs:
Ballylough Castle: Ballylough Castle is a ruined castle in County Antrim, Northern Ireland, that was a stronghold of the MacQuillans and the MacDonnells in former times.

McAllister (surname): McAllister is a surname from Scotland and Ireland that is the anglicised form of Gaelic Mac Alasdair, meaning son of Alasdair.  Alasdair is the Gaelic form of the first name Alexander.  A branch of the MacDonalds or MacDonnells of Ireland and Scotland.  Commonly found throughout Ulster.

Kurtz's Mill Covered Bridge: The Kurtz's Mill Covered Bridge is a covered bridge that spans Mill Creek in the Lancaster County Park in Lancaster County, Pennsylvania, United States.  The bridge is also known as the County Park Covered Bridge, Baer's Mill Covered Bridge, Isaac Baer’s Mill Bridge, Keystone Mill Covered Bridge, Binder Tongue Carrier Covered Bridge, and Mill 2A Covered Bridge.  The bridge is accessible to road traffic from within the park.

Glenarm: Dating back to Norman times, the village is the family seat of the MacDonnells, who once occupied Dunluce Castle on the north coast.  The village is now a Conservation Area, and its main street (Altmore Street) leads directly to Glenarm Forest, from which can be seen Glenarm Castle, on the far bank of the little river which runs through the village to the sea.  The imposing entrance to Glenarm Castle, the Barbican Gate, is at the heart of the village.  The Castle dates from 1750, with early 19th century alterations.  Glenarm claims to be the oldest town in Ulster, having been granted a charter in the 12th century.  The Barbican Gate to Glenarm Castle was restored by the Irish Landmark Trust, a conservation charity that saves buildings that are at risk of being lost.

Blackwater Castle: Blackwater Castle (Castle Widenham) is a privately owned estate located in the village of Castletownroche between the towns of Mallow and Fermoy in North Cork, Ireland, and since 2005 is available to rent as a private hire venue for castle weddings and private parties along with castle rentals for vacations.  The castle comprises one of the oldest occupied castles in Ireland as parts of the residential section date back to the early 15th century while the castle structure itself dates back to the 12th century.  A round tower on the eastern end of the Castle dating from the late 12th century is still standing although no longer accessible.  The castle was constructed on the ancient fortress of Dun Cruadha, an inland promontory fort dating back to the late Bronze Age/early Iron Age, while the site itself was first occupied back in the Mesolithic age (circa 9,000 years ago) as evidenced by the flint scatter found at Kilcummer and the caves on the south bank of the River Awbeg making this site one of the earliest known settlements in Ireland.

Dunluce Castle: Dunluce Castle (from Irish: "Dún Libhse" ) is a now-ruined medieval castle in Northern Ireland.  It is located on the edge of a basalt outcropping in County Antrim (between Portballintrae and Portrush), and is accessible via a bridge connecting it to the mainland.  The castle is surrounded by extremely steep drops on either side, which may have been an important factor to the early Christians and Vikings who were drawn to this place where an early Irish fort once stood.

Raymondville Parabolic Bridge: Raymondville Parabolic Bridge is a historic lenticular truss bridge located at Raymondville in St. Lawrence County, New York.  It was constructed in 1886 and spans the Raquette River.  It was constructed by the Berlin Iron Bridge Co. of East Berlin, Connecticut.  It was closed to vehicular traffic in 1979 was used briefly as a pedestrian bridge.  then closed completely to all traffic for safety reasons.  There is now no public access to the bridge's actual deck, but both approaches are accessible on foot.  There is a nearby similar but shorter version of this bridge also built by the Berlin Iron Bridge Co. still in use linking River Road and NY 56 at Yaleville, New York.  In the late 50's tragedy struck on the parabolic bridge.  A small boy while walking to school one morning lost his footing and slipped on some ice and fell under the railing into the Raquette River where he drowned.

Route, County Antrim: The Route, also historically known as Reuta, Rowte, or in Irish: an Rúta , was a medieval territory in County Antrim, Northern Ireland, consisting of the baronies of Dunluce Upper, Dunluce Lower, Toome Lower, and the North East Liberties of Coleraine (in County Londonderry).  It also formed part of the more ancient kingdoms of Dál Riata and Dál nAraidi, as well as part of the Earldom of Ulster.  It was once ruled by the MacQuillans and later the MacDonnells.

Dunaneeny Castle: Dunaneeny Castle (or "Dunineny Castle", Irish "Dún an Aonaigh") is a ruined castle near Ballycastle, Antrim, Northern Ireland.  The castle was home to the chiefs of Clan MacDonald of Dunnyveg and later the MacDonnells of Antrim.

MacDonnell of Antrim: The MacDonnells of Antrim (Gaelic: "Mac Domhnaill"), also known as the MacDonnells of the Glens, are a branch of the primarily Scottish-based Clan Donald in Ireland.  Initially part of Clan MacDonald of Dunnyveg (Clan Donald South), the MacDonnells of Antrim became their own branch in 1558 when Somhairle Buidhe MacDonnell obtained the lordship of the territory in Ireland from James MacDonald, 6th chief of the Clan MacDonald of Dunnyveg.  The MacDonnells of Antrim were a sept of the powerful Clan Donald of the royal Clann Somhairle, (see Lords of the Isles), that the English crown had attempted to cultivate since the early 14th century in its efforts to influence the course of politics in Scotland.  The MacDonnells established a growing presence in Ireland throughout the 15th and 16th centuries, and played a crucial role in the politics of 17th century Ireland.  Today the surname is predominantly spelled McDonnell in Ireland and abroad.  Many of the present day McDonnells have a common descent from Sorley Boy MacDonnell.

Supporting paragraphs: Glenarm Dunluce Castle
Answer: Dunluce Castle