I'm looking for a good way to mark sections of music piece. Using simple letters such A, B, C doesn't make a lot of sense in "modern" music pieces. Is it still ok to use markings like Verse, Bridge, Intro when there are no vocal parts in the music? Or is there a better way? What are some good practices to do this?
I would recommend against using terms like "Verse," "Bridge," "Intro," etc. unless the piece is clearly referencing that stylistic norm.
Why don't you think A, B, C, etc. make a lot of sense in "modern" music pieces? I've certainly seen it done this way.
Otherwise, plenty of scores simply give the measure number in a large box, thus serving two roles as both a measure locator and an easy landmark by which to lead rehearsals (hence the term "rehearsal" mark).
The reason for using letters (or numbers) is that they are in sequence. If the conductor says "letter D" and the player can see letter B or F, he/she knows whether he/she needs to look before or after that point to find letter D.
A set of terms like "verse", "chorus", "bridge" could be in any random order, unless you are only concerned with a very specific and "formulaic" genre of music.
The letters are the rehearsal marks. Simply naming a section verse, chorus, bridge, ect. is not using rehearsal marks. The purpose of rehearsal marks are to have "a checkpoint" when rehearsing the piece. You are not actually name the section A, B, C, ect., but you are referencing an absolute position on the score to pick up playing the piece in rehearsal.
If you are just talking about labeling sections, you can label the sections however you want. If it doesn't make sense to call them verse, chorus, ect. then don't. It will be up to you at the end of the day.