Step 1: Translate the exam findings into a working diagnosis.
Shortness of breath worsening over a day in a known asthmatic, now gasping and unresponsive, describes a child sliding from severe asthma into respiratory failure and arrest.
Step 2: Use the standard airway, breathing, circulation approach.
After confirming the airway is open, the very next step for a child who is not breathing well enough is to support breathing directly. This means giving breaths for the child, not waiting to see if extra oxygen alone will be inhaled.
Step 3: Test each option against "is the child breathing well enough on their own".
The child is gasping, so the answer is no. Oxygen by mask assumes the child pulls in the gas, which will not happen reliably here. Bag and mask ventilation forces air in regardless of the child's own effort, so it directly answers the problem. Nebulized salbutamol treats the airway spasm but needs the child to breathe it in, which will not happen well during gasping. Intubation is the next step in sequence, done once the child is being oxygenated and ventilated and the team is ready.
Step 4: Rank the actions by urgency.
Bag and mask ventilation buys time and supports the child right away with equipment already at the bedside. Intubation and nebulized therapy follow once ventilation is underway.
Step 5: Conclude.
The first action for a gasping, unresponsive asthmatic child is to ventilate with bag and mask.
\[ \boxed{\text{Ventilate with Bag and Mask}} \]