Regarding taking bribes the Manu Smriti says this:
9.256. Let the king who sees (everything) through his spies, discover the two sorts of thieves who deprive others of their property, both
those who (show themselves) openly and those who (lie) concealed...
9.258. Those who take bribes, cheats and rogues, gamblers, those who live by teaching (the performance of) auspicious ceremonies,
sanctimonious hypocrites, and fortune-tellers,....
The King should reveal those who take bribes by employing methods such as spies and then have to punish them accordingly :
9.262. Then having caused the crimes, which they committed by their several actions, to be proclaimed in accordance with the facts, the
king shall duly punish them according to their strength and their
I have not found any penances prescribed for such offenders yet.If found will update the answer with them.
Anyways,taking bribes is illegal as per Dharma Shastras and the king should act and punish the offenders accordingly.This is the directive of the Shastras.
Update regarding penances:
There are no penances prescribed specifically for bribery in Manu and the Parashara Smritis.There is nothing in the Yajnavalkya Smriti either(however i only have an abridged version of it).
The Manu Smriti however itself says that there can be many offences for which no penances have been prescribed in it.And,in those particular cases the offender can decide(the mode of atonement) on his own :
Manu Smriti 11.209. For the expiation of offences for which no atonement has been prescribed, let him fix a penance after considering (the offender’s)
strength and the (nature of the) offence.
In general,the Manu Smriti prescribes:
Manu Smriti 11.227. By confession, by repentance, by austerity, and by reciting (the Veda) a sinner is freed from guilt, and in case no other course
is possible, by liberality
So,charity can be a good enough atonement in my opinion.
Update #2 regarding paying interest:
Paying interest, lending money on interest are not sins.But ,usury, the act of lending money with unreasonably high interest rates is a minor sin(an upapataka).
Manu Smriti 8.140. A money-lender may stipulate as an increase of his capital, for the interest, allowed by Vasishtha, and take monthly the eightieth
part of a hundred.
Manu Smriti 8.142. Just two in the hundred, three, four, and five (and
not more), he may take as monthly interest according to the order of
the castes (varna).
1.61. Manu Smriti:Defiling a damsel, usury, breaking a vow, selling a tank, a garden, one’s wife, or child, are(minor) sins.
Similarly,from the Yajnavalkya Smriti:
There are many Upapātakas (minor sins and turpitude). They are:—
stealing a brahmin's personal effects, non
payment of debts.....learning from a servant, teaching a superior,
adultery, usury, sale of salt, contemptuous livelihood,
misappropriation of a deposit,.....all these are Upapātakas.