The commencement of an action may itself indicate the unspoken verb. Saying bi-smi llāh as one begins a task is interpreted through that task.
Before recitation, one may understand bi-smi llāhi aqraʾu, “in God's name I recite,” or an equivalent formulation. At the beginning of a meal, a suitable interpretation involves ākulu, “I eat.”
The spoken words are identical; the situation of utterance selects the intended action and makes lengthy explicit wording unnecessary.
Grammatically bi is a preposition, ism its genitive noun and Allāh the genitive complement; the action supplies their attachment.