I'm surprised all vendor variants seem to show a sliced bagel -- either closed with a filling or two separate halves with or without a filling.
A bagel is not necessarily sliced, and a good fresh bagel can be beneficially eaten like a pretzel without slicing it at all.
If I were the designer given the brief "generic iconic bagel", I would not have it sliced at all, thus avoiding the question of whether or what filling. I would put some seeds (sesame or poppy, either way) on it, to help distinguish from a doughnut.
And yet, all actual variants are sliced. Odd. Does unicode provide a suggested schematic for these, that perhaps suggests sliced?