You can take a bus from Bibury to Burford via Northleach, Market Place in around 1 h 36 min.
How to get from Bibury to Burford
From Bibury, Bridge House line 855 bus to Northleach, Market Place then line 853 bus to Burford, Oxford Road Layby (Burford Roundabout). 1 h 36 min £6. From Bibury, Bridge House line 855 bus to Bourton-on-the-Water, War Memorial then bus to Burford, Church Lane. 2 h 10 min £8. From Bibury taxi to Burford. 12 min £33. From Bibury drive to Burford. 12 min £1.