The error in this sentence is a Misplaced Adverb. An adverb should be placed as close as possible to the word it modifies to ensure the meaning is clear.
In the sentence, "Politely, she takes the bus to work," the placement of the adverb "Politely" at the beginning of the sentence suggests that the act of taking the bus is a polite action, which does not make sense in this context.
The intended meaning is likely that she speaks or behaves politely, or perhaps she takes the bus quietly. However, if the adverb is meant to describe her manner of traveling or her interaction with others, it should follow the verb or be placed at the end of the clause. If the sentence meant she is a polite person in general, an adjective would be used (e.g., "She is polite"). Placing it at the start as a sentence adverb changes the logic of the action "taking the bus."
Incorrect: Politely, she takes the bus...
Correct (Contextual): She takes the bus to work regularly (Frequency) or She quietly takes the bus to work.