This question is based on the provisions of the IPC as they stood before the Prevention of Corruption Act, 1988, consolidated the law on bribery.
Section 161 of the IPC (now repealed) made it an offence for a public servant to accept an illegal gratification.
Abetment (defined in Section 107, IPC) includes instigating someone to commit an offence.
By offering a bribe to B, A is instigating B to commit the offence of accepting an illegal gratification under Section 161. Therefore, A has abetted the offence defined in Section 161, IPC. The other sections dealt with different forms of influence and gratification. Today, both giving and taking a bribe are substantive offences under the Prevention of Corruption Act.