I have been testing out different variations of inserts lately, but for nighttime use. So, bulkiness isn't a concern for me.
But....I have found that the organic cotton inserts that come with the Flip trainers (not regular Flip covers) actually work well inside the BG pockets! Very trim, too, plus, no folding required!
For nighttime, tho, I do like HempBabies flats and also Rumparooz Bamboo inserts. I just bought a couple of these pricey bamboo inserts from a local seller, but I think they may be worth it!