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When you select a midi style (I guess also RealStyles) how do you know from the list of instruments shown for the style, which one goes on which part - bass, piano, drums, guitar, strings?

The same exact thing was bothering me yesterday. You can see the correlation by ticking the part in the chord sheet - the associated midi patch and RT, if there is one, are shown just below - but there's no way to switch between parts when the stylepicker is open. (I think programmers would call it a modal window.)

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Is there some way to ensure that the instruments as shown are automatically selected to the proper parts?

Not that I can see. They'd have to be assigned manually if you want a different allocation than is defined inside the style. I'm afraid the "part" names are one of those conceits from early BB versions, where they conveyed more meaning than they do nowadays with all the newfangled styles and RTs. The part names are, after all, just designations for (assignable) midi channels.