Does the bishop have a job if the country is a royal colony?

Nearly all countries have bishops working there -- often several, and of different religions. It doesn't depend on their status as a crown colony; bishops are generally unaffiliated with the local government, but instead are employees of the central church authority. For instance, all Catholic bishops work for the Catholic Church, based in The Vatican.

There's a bishop wherever there are enough parishoners of their religion to support one (if that religion has bishops); the government only matters if the government doesn't tolerate their religion. British colonies don't outlaw any normal religions (assuming that's the crown you meant).