What is the normal recovery period after a hip bruise?

Varies. Minor and superficial bruises are much better within a few weeks. More severe and deeper bruises can take several months to completely recover.
A few days. Hip bruise is a vague term that is hard to interpret in terms of severity of damage and the type of structures involved. If you are talking about a strain, an uncomplicated one should take a few days to a week or may be two to heal. If it's a large hematoma (blood in the muscle or under skin) and there is more severe damage, there may be more time needed to heal.