The Bath bun sandwich starts from a bread that is already sweet, and that single fact governs everything about it. A Bath bun is an enriched, slightly sweet roll, traditionally crusted with sugar nibs and sometimes carrying candied peel or a sugar lump baked into its base. Splitting and filling it means the bread is not a neutral carrier the way sliced white is; it is a flavoured component with its own sugar, and any filling has to be chosen knowing the bread will not stay out of the way. The bun is the loudest thing in the sandwich before anything goes in it.
The craft is balancing a filling against a bread that is already sweet and fragile. The plain build splits the bun and spreads it with butter alone, treating the bun and its sugar nibs as the whole point, and salted butter is doing real work here, the savoury note that keeps a sweet crumb against sweet butter from collapsing into one flat register. Where a filling is added it leans on contrast: clotted or whipped cream and a little jam turns it toward a cream bun and a West Country tea plate; a tart fruit compote cuts the bun's sugar rather than echoing it. The bun is rich and tender so it tears rather than slices cleanly and does not survive a heavy or wet load, which is why the fillings that suit it are light and either creamy or sharp. The sugar crust on top is structural to the experience: it is the crunch against an otherwise soft sandwich and the reason the bun is filled split rather than crumbed open.
The variations stay close to the tea table. Butter only, clotted cream with jam, and a lemon-curd fill are the standard moves, each working with or against the bun's own sweetness rather than ignoring it. The closely related Sally Lunn, a larger and plainer enriched bread from the same city, takes savoury and sweet fillings more readily. Those deserve their own article rather than being crowded in here.