When I am eating a meal alone and that meal includes bread what parts of the Birkat Hamazon do I pray? Which parts do I exclude? And please be specific. (I use the Schottenstein Artscroll siddur hachol.)
The same bentching as when not alone except the invitation part called a "zimun" which is said when there at least males present that are at least bar mitzvah age or older.
You Bentch the same Bentching you'd normally do except without the zimmun (רבותי נברך), and if you are eating in your own house you'd say Harachaman who yivaraych osi. You can probably find this in the Artscroll Siddur, and most Bentchers.
You would the normal Bircas HaMazon, minus the Zimmun (Invitation; Rabosai Mir Velen Bentshen or Rabosai Nevarech). If you ate something that was not bread, but made of grain, such as a small cake, recite the three faceted blessing.