If your opponent wants a zombie, they can choose to receive one. If they don't want one, they can choose to not receive one.
When reading a card's activated ability, you will see that different parts of the ability's cost are separated from each other by commas. Each such part is a separate component, and when an activated ability has more than one component to its costs, those different costs can be paid in any order relative to each other.
Insolent Neonate's ability has two components: “Discard a card” and “Sacrifice Insolent Neonate”. If your opponent discards a card first, then
Bridge from Below will be in their graveyard at the time the Neonate is sacrificed and will therefore trigger. If for whatever reason they decide to sacrifice the Neonate first instead, then the Bridge will not enter their graveyard until after the Neonate has already died, and therefore will not trigger.