If a person feels biased when asked to mediate a conflict, they should handle the situation with honesty and integrity. Here are the steps they can take:

1. **Acknowledge the Bias:** Recognize and admit to themselves that they have a bias. This self-awareness is crucial.

2. **Communicate Openly:** Inform the parties involved in the conflict about the potential bias. It’s important to be transparent so that everyone understands the situation.

3. **Decline the Role:** If the bias is significant enough to affect impartiality, it’s best to step down from the role. Suggest finding a neutral third party to mediate instead.

4. **Offer to Assist in Another Capacity:** If possible, they can offer to support the process in a different way, such as helping to find a suitable mediator or providing background information.

5. **Reflect on the Bias:** Consider why the bias exists and whether it can be managed or mitigated in a way that still allows for fair mediation. If the bias is minor and can be controlled, they might still be able to proceed but with extra caution.

Being upfront and prioritizing fairness is essential to maintaining the trust and integrity of the mediation process.