For a bedroom is it Length x Width, or Width x Length?

The smaller number is the width and the larger number is the length.

the longest measurement is the length as in anything carpet comes in widths its on a roll and cut to lengths 8ft 8" would be the width and the carpet would be cut at 12ft and a bit for cutting to fit as the width would need cutting

Carpet is sold by sq yds. Either of your calculations is correct when rounded up to 9 x 12 feet= 108 sq ft. /9 = 12 sq yds. As most carpet rolls are 12', you need a 9' section, but it will be priced by the yard except perhaps off the roll at a home improvement store.

What is the width of the carpet? You want to select the width of the room that best fits the width of the carpet. Then the carpet is cut to the length that extends the length of the room so that you have a carpet with no seams. So, if carpet comes in a roll 12' wide, you want a piece of carpet 8'8" long. You cut the 12' width back 3" to give you 11'9". And since the walls aren't straight you need a little for adjustment, but you should have it. And, of course your pattern in the carpet has to be appropriate for the way the room lays out. Like stripes should be with the length of the room.