The Spalding Club's 'Place-names of Aberdeenshire' gives the following spellings from various documents:
1362 - Badcass
1376 - Badochayse
1493 - Badycaiss
1593 - Badaquhasche
1737 - Badiechash
It says "the oldest form would be bad cas, winding or steep wood. The changes from that to the present Baldyfash are all more or less normal to Aberdeenshire speech. Baldy-, pronounced Bady-, may represent badan, diminutive of bad, wood, clump of trees."