Translation:The river flows sluggishly under the bridge.
sub + ( Accusative, Ablative ) • Which Case depends on whether or not the expression context means the [ Subject - Verb - Preposition: Direct / Indirect Object ] interaction is Transitive in nature. Does the Preposition transfer the Subject's Verb action to impact or bear upon the Object? If yes, then Transitive - Direct Object in the Accusative Case. If no, then Intransitive - Indirect Object in Ablative Case.
river flows to the bridge • Accusative
river flows under the bridge • Ablative
A cat runs around inside the barn • Locationality - no from-to transit directionality
A cat runs to the barn • Accusative, from-to transit directionality
Conceptually it is normal that the river water always flows under the bridge. Although, with sufficient flooding, the river could flow over, around, under and through the bridge.
In this expression, [ sub ponte ... fluit - under the bridge ... flows ] conveys the where - location of the Subject Verb activity - not - to where -> directionality
The river flows to the sea. • To where? Transitory, Accusative