Hmmmm.
Modern gazetteers are as good as useless when it comes to finding single 19th censtury or earlier houses, farms or crofts, so I am not surprised that you have drawn a blank there.
The gazetteer at
http://www.abdnet.co.uk/genuki/BAN/Alvah/locations.html doesn't pinpoint it, but I think we can do better.
In the 1881 census there is one listing of Bridgend, parish of Alvah, in ED4. In the same ED are Burreldales, Lintmill, Newton, Pole of Itlaw, Itlaw Smithy, Bagra, Greenlaw, Waulkmill, Auchinbadie, Hungryhills, various bits of Mountblairy, Boggiehead, Brownside, and Maryhill. This puts it in the southern part of the parish of Alvah, next door to Forglen.
ED 3 includes among others Linhead, Roberton and Rosieburn, so the boundary of ED4 must follow the B9121 road south of the Pole of Itlaw, with ED4 to the east and ED3 to the west. You can check the exact boundaries of each ED by looking at the start of the pages for each ED in the census.
Various 20th century maps show a place named Bridgend of Mountblairy, just a short distance from Pole of Itlaw. There is no mention of Bridgend of Mountblairy in either the GENUKI Gazetteer or the 1881 census.
The late-Victorian six-inch map of the area shows both Lintmill and Newton as 'of Mountblairy' even though neither the 1881 census nor the modern maps include 'of Mountblairy'. So it is not impossible for a place's name to change over time by the subtraction of a suffix, or for different variations of a name to be used in different places around the same time.
It also shows Bridgend of Mountblairy. By the same process whereby Lintmill and Newton lost their suffixes, Bridgend of Mountblairy was probably known locally as just 'Bridgend'. Why bother to say or write 'of Mountblairy' every time, when everyone knew the place just as Bridgend?
Therefore I think that your Bridgend Cottage is or was almost certainly at the farm or croft which is named on modern maps as Bridgend of Mountblairy.
To see where it is, go to
http://www.geograph.org.uk/gridref/NJ6856Click on the map and the more detailed map in the pop-up window will show you where Bridgend of Mountblairy is.
If this isn't conclusive enough, there are other ways of verifying the location.
You could search for the address in the 1891 and/or 1901 censuses, and note the name(s) of any householders at Bridgend/Bridgend of Mountblairy. Then go to the valuation rolls for 1885 (also available on Scotland's People) and check the name of the householder against the address.
You will almost certainly find that the proprietor then was Mountblairy Estate; if so it might be worth contacting the estate office to ask whether Bridgend Cottage and Bridgend of Mountblairy are/were one and the same.
