Ballyministragh is a townland. A townland is an Irish administrative unit. Ballyministragh consists of 784 acres of mainly agricultural land. (There isn’t a town in the townland).
I had a look at the revaluation records for Ballyministragh around 1901. There’s no sign of Charles Bowman being listed. That could be because he didn’t live there very long or possibly because his house was of too low a value to be listed.
https://www.nidirect.gov.uk/services/searching-valuation-revision-books
Looking at the 1901 census, I can see that his house was single story, with 2 to 4 rooms and 2 windows at the front. So a typical labourers cottage. His landlord was Mary Jane Minnnis. She is listed in the revaluation records. Her farm was plot number 8 (a 24 acre farm). So it appears that the Bowmans had a small cottage on her farm. The Minnis property today is up a dead end lane off the east of the Killinchy Rd. It overlooked a small lough, though whether the lough is still there isn’t clear from the modern map. The lane turns off the Killinchy Rd just south of Rose Cottage.
You can see where it is using the maps on Griffiths Valuation.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
The Bowmans cottage is probably long gone (most fell into disuse as the need for labourers diminished) but the Minnis farm may still be there.
Ignore the house number in the 1901 census. Houses in rural Ireland didn’t have any numbers in the early 1900s (and in some areas they still don’t). The townland name was sufficient to identify you or get a letter delivered. So when the census enumerators arrived they made up their own private numbering system (which varied from census to census) but which has no relevance to Griffiths or any modern house numbers (which were generally allocated in the 1960s).
You asked about Old Meeting House Green. I don’t know the location but a Meeting House is the term used by Presbyterians to describe their church. And a green is obviously a grassy area often used for public purposes. So it’s somewhere near an old Presbyterian church. There’s a Presbyterian church in Ballyministragh, plus a Non Subscribing Presbyterian church (often known as Unitarian). So I suggest you scour the local area for old Presbyterian churches and see what you can find.
As to the origins of the name, I can’t say with absolute certainty but it is name commonly found in Scotland (there’s around 2000 of them in the 1901 Scottish census), they were Presbyterian and they lived in Co Down, which was very heavily settled by Scots in the 1600s. Presbyterianism was established in Scotland by John Knox in the 1500s and brought to Ireland by the Scots settlers. Looking at all these factors togeter, my money would therefore be on Scottish ancestry. (Well over a half the population of Co Down are of Scottish descent. It would be the most common origins for that county).
