Looking at the Bard progression table, Bards begin at level 1 with 4 spells known, and then gain (on average) 1 new known spell per level, until they cap at level 18. I'd like to know if there is a rule or guidance on how a bard could gain one single extra known spell through some kind of special training? For example, time between adventures can be spent to learn a proficiency in a new skill by spending 250 days (at 1gp per day) to train in said skill. Is there something similar for known spells?
I'm not looking for extra cantrips or spell slots, and I know the Magic Initiate feat can grant such an extra known spell (and casting it at level 1) if taken in the same class, in addition to 2 cantrips. But I'd like to avoid going as far as a feat for that.