A bourdon tone is added to this Hildegard antiphon because it's thought likely (or at least possible) that it was performed this way originally. While there is no direct evidence for this practice in Hildegard's music, it is found (written out) in much other medieval music- for instance, in the organa of the Notre-Dame School. Also, a bourdon or drone was built in to a lot of instruments (bagpipes, fiddles, hurdy-gurdys), and still exists in a lot of folk music. Besides, it sounds good (I perform Hildegard with drones). Whether this is reason enough to add bourdons to Hildegard, everyone must decide for themselves.
This antiphon is, very typically for Hildegard, in a mixed Aeolian/Phrygian mode based on A (in the score). Thus, the tone A would be appropriate for the bourdon if singing at written pitch.