Your seem to ask for "Polygon Bearings" in the post title, but you also stated that "I'm trying to find the bearing of a property line...". I was guessing you actually need bearings of polylines, likely straight lines as property lines. If your starting point is parcel polygons, I am not sure if there is any tool specifically made for breaking parcel polygon boundaries into straight lines; but you can have a look of the following tools:
- Feature To Line
- Polygon To Line
Both tools are in ArcToolboxes (System Toolboxes) - Data Management toolbox - Features toolset, requiring ArcInfo license.
The Minimum Bounding Geometry tool is new in ArcGIS 10; you can find it in the same tool location. I mention this tool to you only in case you can't find any other way to get the bearings. But please note: this tool gives you "orientation" not "bearing". The difference: a bearing is based on the direction of a line; an orientation doesn't take into account of a line direction. So some of the orientation values you get from this tool may be 180 degrees opposite from the bearing values. It would take visual inspection to find them and recalculate the values. So this workaround may not be efficient if you have a large dataset to process.
Regards,