The original source is a 4-koma or four-panel comic strip collected into magazine "volumes" by Manga Time Kirara MAX. There is no official English translation that I can find, and English translations can be found on the usual websites.
I am not a fan of the 4-koma type of manga. The format looks like a cheap web 'toon or a story meant to be read on your smart phone. The four panel style limits the amount of information that can be included. It is a stripped down or spare manga. This is just my personal prejudice against 4-koma, and your mileage may vary.
With a successful anime, it is possible that that there will be interest in a full manga adaptation. It has happened for other 4-komas. For now, the reason to search out and read the inadequate translations of this 4-koma is if you love the anime and want to get all the details of the original story. Just be aware of the limitations of the 4-koma and don't expect something as polished as the CloverWorks anime.
Another thing about this that makes me keep coming back: the author is always showcasing real bands, and I keep looking them up on Spotify. I've discovered some great music from the author's endorsements in the pages of Bocchi the Rock! So don't just skip over the photos of IRL bands. Look them up and maybe expand your playlists.
