What Does Bushing a Clock Mean?
If a clock movement does not get serviced (cleaned and oiled) routinely it will over time cause wear in the plates of the movement where the pivots come through. These can be easily noted as they usually are oval shaped instead of round. A clock that is need of bushing runs erratically if at all. Bushing consists of replacing the worn brass around the pivot so that it is round again.
What does staking a clock mean?
In the past clock makers used to "stake" the oval shaped hole to make it round again. This consists of using punches and a hammer to push the oval shaped brass plate back to round (note the holes around the pivot in the pics below). Staking is now frowned upon as there are better ways to restore the hole to round. Below is a pic of a plate that has been staked: