Do bilbies live in the tropical rainforest?

No. Bilbies do not live in the tropical rainforest.

Bilbies live in burrows in hot, dry grasslands and semi-arid spinifex areas. The burrow entrance is often positioned against a termite mound or small shrub, and a single bilby may have up to a dozen burrows that it uses either for shelter during the day, or as a quick escape route from predators.

Amazingly adaptable for their size and the threats to them, bilbies can live in sandstone ridges, gibber plains, rocky soils with little ground cover, a variety of grasslands, and acacia scrub.