Can I enter Bhutan by land and exit by air (or vice versa)?

Yes, you can enter Bhutan by land and exit by air or vice versa.

Land Entry or Exit points in Bhutan with its counterparts in India

1. Phuentsholing :  Jaigoan, Alipurduar district, West Bengal on the India side.
   Located 155km/4+hrs drive from Bagdogra airport.
2. Samdrup Jongkhar  : Darranga, Tamulpur district, Assam on the Indian side.
   It is located about 100km/3hrs drive from Guwahati airport.
3. Gelephu (Mindfulness city) : Hatisar, Chirang district, Assam
   Located 230kms/6hrs drive from Guwahati airport