Learn English – Adjective that means “snake-like”

Serpentine is the snake equivalent of bovine.

of or resembling a serpent (as in form or movement)

_{Source: http://www.merriam-webster.com/dictionary/serpentine}

Serpent - synonym of snake

Wikipedia :

Snakes are elongated, legless, carnivorous reptiles of the suborder Serpentes
...
All modern snakes are grouped within the suborder Serpentes in Linnean taxonomy,

Whereas Ophidia is a supergroup of lizards and snakes.

Ophidia is a group of squamate reptiles including modern snakes and all snake-like "lizards" closer to snakes than to other living groups of lizards.

I would however likely use reptilian or snake-like for descriptions of behaviour, viz her bovine eyes looked calmly at me