I would use the garage for several reasons:
1) As you said, it's close to the bathroom and no power additions are needed.
2) An outbuilding is not as secure as the garage can be
3) To run power out to the outbuilding, you would need an electrical permit, probably an electrician and an inspector before you could use start using the outbuilding. When you also take into consideration that only specific types of wire can legally be run underground(and they are not cheap), the cost outweighs the benefits of having a dedicated area to work in.
4) A power garage door opener can normally be unplugged, that is unless it's hard-wired in