What if someone reports bullying or harassment to me?

Listen without judgement. Offer support, try to never leave them feeling alone. Seek help and if you can, explain the options to them.
Be clear about the limits of confidentiality as you may need to disclose information to other appropriate parties (e.g. HR, Student Support Services). So try not to make a promise that you may then need to break. And if you feel that there is the risk of serious harm you need to call for help.
Suggest other sources of support e.g. Harassment Advisors, The Employee Assistance Programme (Spectrum.Life), Staff Gateway, Occupational Health
Outline their options including informal and formal processes. Look at the harassment flowcharts for more information.
If the a member of staff feels unable to do any of the above at this stage, they could report anonymously Report + Support. This may not provide a remedy, but it could give them some time to consider if they wish to follow one of the processes above.