Is there a certain rule as to when to trim bushes? The bush I want to
trim is blooming and is blocking entrance to my garage so I'd like to
trim it. Any general rules? Should I wait until the bush stops
blooming?

More oft than not you would be fine to do a pruning at just about any time
of the year. Harsh prunings should be put off until right about the dormant
season to allow the plant time to prepare to go dormant. For example, I'll
be going out this evening to prune up some honeysuckle, a couple of red bud
trees, and a sunburst locust. Most folks don't prune when a shrub is in
bloom to maintain the beauty of the plant for the blooming season.

There are some trees and shrubs that are a bit particular about pruning
though and you do not mention what kind of bushes these are in your
posting...?

James