Thanks for your replies.
My grandfather, Walter Bibby, died young and my grandmother remarried to Tom Morris. The marriage certificate to Walter Biiby states her father as Edward Anderson but there is no mention of her mother. Every search I try there is no documentation and it is only hearsay that her mother was Sarah Livermore. I think the only way I will know for certain is if someone knows through family history. I think it is more difficult to trace traveller families due to the nature of their lifestyle, especially over 100 years ago.
Thanks again for your help.