Take the main road 205 through Esrum, or the main road 227 towards Esrum.
You can catch the Lokaltog 950R which runs between Hillerød St and St Gilleleje Lokalbane 950R see timetable.
Disembark Saltrup St. with your bike and take the beautiful trip of 3.9 km to Bird Park. Most of the journey will be on gravel paths.