My question is explicitly asked by the Chavos Yair (as I've found based on your great reading suggestions):
לכאורה יש לתמוה למה לא הזהירה תורה גם לא תתן שוחד כמו דהזהירה גבי
Seemingly it is surprising that why haven't the Torah forbidden giving
bribe just as it forbade giving interest?
The answer is quite lengthy but I believe that its core is that since by bribery the Torah have specified a reason (not to pervert the judgement), therefore it is incumbent on a future event (whether the judgement will be perverted or not). Therefore there is a chance under certain circumstances that it is not causing a problem.
This is not the case regarding interest where the wrongdoing is committed immediately and the person giving and taking are committing it, and it has nothing to do with the future.