to atone / pay a fine
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to atone for
To bear the negative consequences for an offense, guilt, or sin and thereby make amends for it. It often has a moral or religious dimension.
Er war der Überzeugung, für seine Taten in der Jugend ein Leben lang büssen zu müssen.
He was convinced that he would have to atone for his actions in his youth for the rest of his life.
The verb 'büßen' (to atone, to pay a fine) is closely connected with the nouns 'die Buße' (atonement, penance, punishment) and 'das Bußgeld' (fine). This connection helps you understand both meanings of the verb.
Für seine Fehler musste er teuer büßen.
He had to pay dearly for his mistakes.
In the moral meaning 'to atone', 'büßen' (to atone) is always used with the preposition 'für' followed by the accusative. You always atone 'für' (for) an act or a sin.
Im Roman muss der Held für die Sünden seiner Vorfahren büßen.
In the novel, the hero must atone for the sins of his ancestors.
The meaning 'to atone for guilt' belongs to an elevated, often literary or religious style. It is rarely used in normal everyday life.
Der Priester sagte ihm, er müsse für seine Lügen büßen.
The priest told him that he had to atone for his lies.
When it is about a monetary penalty, 'büßen' (to pay a fine) is often used directly with the amount as an accusative object. For example, you can say '50 Euro büßen' (to pay a fine of 50 euros).
Wenn du zu schnell fährst, musst du ordentlich büßen.
If you drive too fast, you'll have to pay a hefty fine.
to bathe / swim
'etwas ausbaden müssen' and 'für etwas büssen' can both mean that someone has to bear negative consequences. The difference lies in the tone and the reason. 'Etwas ausbaden müssen' is often used in everyday language, especially when someone has to deal with the consequences of a mistake that maybe someone else made. 'Büssen für' sounds more serious and often has to do with guilt, punishment, or morality. When it is about an everyday unpleasant consequence, 'ausbaden' sounds more natural. When guilt and punishment are at the center, 'büssen' fits better.
Der Fahrer hat für seinen gefährlichen Fehler schwer büssen müssen.
The driver had to pay dearly for his dangerous mistake.
Weil der Kollege den Termin vergessen hat, muss das ganze Team den Fehler ausbaden.
Because the colleague forgot the appointment, the whole team has to pay for the mistake.