My question is, how can this section be best analysed with Roman numerals? (I would imagine something like "V/?" "I/?" would be better than simply writing "bVII" "III".)
I wouldn't choose bVII-III, but V/I B (D!) or V7/iii ... both are adequate.
Like most minor pieces this passage in B-minor includes the relative major chord D = III. You will encounter this "modulation" which is actually only a short extension to the relative key by its secondary dominant A7->D (V7/III) in almost every choral by Bach or tune by Handel's Concerti Grossi in minor. As the melody doesn't remain for more than some bars in this new key it's better to say V7/III than V7/I of D, but it wouldn't be wrong, both analyses would be accepted and understood.
(b.t.w. every other degree can be reached by its secondary dominant, also in a major key!
In C major you often find an analogous situation: starting with the tonic C and leading to the relative key/chord like C-G-C-E7-Am-C7-F ... which is I-V-I-V7/vi-vi-V7/IV etc)