Learn English – A single word for “moved around a lot”

The answer is in the definition of drawbridge:

a bridge of which the whole or a section may be raised, lowered, or drawn aside, to prevent access or to leave a passage open for boats, barges, etc.

_{Source: http://www.thefreedictionary.com/}

Moveable bridge and drawbridge are synonymous but drawbridge is also a specific type of movable bridge. It is the most common type.

Also, you might use different verbs for some of the specific types of movable bridge. The picture you provided is a swing bridge and you might use turn or rotate.

"Open" and "close" depends on the point of view. You would say "open for cars" or "open for boats" to be clear about what you mean. This is also mentioned in the definition of drawbridge.

Note: There isn't a single verb that you can use for all movable bridges and that would clarify the situation, at least not in common usage. There is an adjective trafficable which defines something that can be traveled upon but it wouldn't be used in everyday speech.

I can see the usage of connect/disconnect and lock/unlock in technical usages but these terms are more related to the mechanisms of movable bridge than accessibility.

Busywork is a general term for this, but doesn't quite capture the disparity between his abilities and assignment. Link-MW

The military has many colorful, pithy expressions for this sort of thing. "Counting dolphins", "piloting a desk", "interrogating the snow", etc.