Bast sounds to me like a natural textile thing.
Rohr is a tube, or rather a cane.
So it’s that grassy stuff that you use to make baskets.
Wiktionary has a good etymology for "bast":
From Middle English bast, from Old English bæst (“bast, inner bark of trees from which ropes were made”), from Proto-Germanic *bastaz (“bast, rope”) (compare the Swedish bast, Dutch bast, German Bast), perhaps an alteration of Proto-Indo-European *bʰask-, *bʰasḱ- (“bundle”) (compare Middle Irish basc (“necklace”), Latin fascis (“bundle”), Albanian bashkë (“tied, linked”)).
This is a Latin fascis:
People often say that it’s a bundle of sticks, but I would say it’s more like reed (Riet in German). Hollow, quite flexible tubes that are actually hard to break; they bend but do not break. And if you bundle them, they don’t even bend any more, that makes the image of fascis for fascism even more powerful for a collectivist statist ideology. Digressing a little, but it’s to illuminate the full spectrum of why I intuitively thought of Bast as a textile rather than a stick.
And Rohr is just emphasizing that its a reed, or in German a Halm; think of Strohalm for drinking straw.