Bribes could be a crime is fail, depending on the wealth, position and responsibility of the target. You could bribe beggars and it would rarely fail unless they hated you and the bribe was low, same with other people with low responsibility but the amount would be much higher. Fail would give a large reputation drop and it would be hard to bribe somebody who hate you, high risk for fail even with a high bribe, but easy to bribe somebody from reputation 60 to 70.
Now if you try to bribe guards or public figures, this might be dangerous, if bribe fails they would arrest you, again success depend on your charisma, speechcraft, how much they like you, their responsibility and wealth as a rich npc would see a 10 gold bribe as an insult. Some npc like Lex would not accept a bribe. Now make charm far harder, perhaps make it more of an hostile spell, treat it like pick pockets a crime if noticed. An area effect spell cast from behind cover in sneak mode would usually succeed, cast it in their face and they will behave normally until the effect wear of then react negatively.
One other idea is to make chameleon and invisibility inside cities unpopular and illegal inside houses unless on quests (not thief guild or brotherhood quests
.