Triggers execute within the SQL engine. Bulk-binding impacts the way that the calling language (pl/sql or any OCI language) calls the SQL engine, by reducing the number of calls/statements, but should not bypass any triggers.
(Imagine you have used a trigger to add validation, logging or other constraint to a database, but a third-party application would bypass it simply through using a bulk operation - this would be a recipe for data corruption and security issues).
Your statement level trigger should fire once.
You could 'disable' your trigger by making it check an in-memory session variable before doing anything else, and explicitly setting it before a bulk operation.
Row level triggers would still fire on a per-row basis, which could have a lot more impact.