The bap is the soft option, and that is the whole point of it. A bap is a round, white roll with a yielding crumb and a thin, dusty bloom of flour on top, baked to be pillowy rather than crusty. It tears instead of cracking. Press your thumb into one and it gives, then slowly comes back. Where a stiffer roll holds its shape against the filling, the bap is built to surrender to it, which is exactly the behaviour you want under a few rashers of hot bacon. The bread is the variable that defines this sandwich; the bacon inside is the constant that every region agrees on.
What the bap does well is absorb without collapsing. Bacon, fried until the fat has rendered and the edges have caught, carries a film of hot grease and salt that has to go somewhere. A baguette would shatter and a heavily crusted roll would resist it; the bap drinks a measured amount into its lower crumb and turns slightly translucent there, holding the rest rather than letting it run down a wrist. The build is plain on purpose: the bap is buttered to the edges while still cool so the fat does not soak straight through, the bacon goes in hot off the pan, the sauce goes inside rather than on top so it stays put, and the roll is closed and eaten before the steam has finished softening it. The flour on the lid stays dry and faintly chalky against the lip while the base has gone rich and dense, and that two-texture contrast across one small roll is the appeal.
The same sandwich answers to other words a few counties in any direction. In Lancashire the roll is a barm; across the East Midlands it is a cob; around Coventry and Liverpool it is a batch; in Scotland it is a morning roll, and in the Northeast a stottie. Drop the bread question entirely and the soft-bread version is just a bacon butty, or a bacon sarnie if you are being casual about it. The fillings stretch the same way: a fried egg with a yolk to be managed, a sausage alongside or instead, brown sauce against red as a settled household disagreement. Those deserve their own articles rather than being crowded in here.