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The drones in the hive are her brothers. She needs more gentic diversity, so she goes out to mate with other colonies' drones. Her attendants know where to go find them because they've scouted them before.

The drones are also clones (?) of the prior queen. They are unfertilized eggs, so they contain a genetic copy of half the queen's DNA. Mating with a drone from you hive would be like mating directly with your genetic mother. It's going to result in real bad inbreeding real quickly. Especially since queens mate a single time, and live for only a few years.

They're like half-clones, yeah. Queens can mate more than once though, but usually just once, and if more than once just twice. A well-mated queen will have sperm from a dozen different drones.

Ahh, thank you, I thought she mated with her own drones and was wondering how they got any genetic diversity like that.

I think two answers, though as per TFA there's probably a lot more behind this:

First, she wants to get the best genetic material, and flying high is one of those tests for drones to pass, and

Second, needs to acquire genetic material from different bloodlines, hence does the business with several drones (obviously not an option within the hive).

Maybe for the same reason we don't marry our cousins? :)